Finite Group Databasebeta

← Group #11775327

Character table — Group #11775327

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1111222222222222222244444444444444444668888888888888888888888812121212121212121212122424242424242424242424242424484872727272
order12222233446666666666346666666661212121212122244121212121212121212121212121212121212121212244666612121212444488121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ91111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-111i−iii−i−i111-1-1iiiiii−i−i−i−i−i−i-11-111-1-111-1-11-1i−ii−iii−i−iii−i−i1-11-1i−i
χ101111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-111i−iii−i−i111-1-1iiiiii−i−i−i−i−i−i-11-111-1-111-1-1-11i−i−iiii−i−i−i−iii-11-11−ii
χ111111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-111−ii−i−iii111-1-1−i−i−i−i−i−iiiiiii-11-111-1-111-1-11-1−ii−ii−i−iii−i−iii1-11-1−ii
χ121111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-111−ii−i−iii111-1-1−i−i−i−i−i−iiiiiii-11-111-1-111-1-1-11−iii−i−i−iiiii−i−i-11-11i−i
χ131111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-1-1-1i−iii−i−i111-1-1iiiiii−i−i−i−i−i−i1-11-1-111-1-1111-1−iii−i−i−iiiii−i−i1-1-11−ii
χ141111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-1-1-1i−iii−i−i111-1-1iiiiii−i−i−i−i−i−i1-11-1-111-1-111-11−ii−ii−i−iii−i−iii-111-1i−i
χ151111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-1-1-1−ii−i−iii111-1-1−i−i−i−i−i−iiiiiii1-11-1-111-1-1111-1i−i−iiii−i−i−i−iii1-1-11i−i
χ161111-1-111-1-1111-1-11-1-11111-111-1-1-11-1-111-1-1-1-1-1-1−ii−i−iii111-1-1−i−i−i−i−i−iiiiiii1-11-1-111-1-111-11i−ii−iii−i−iii−i−i-111-1−ii
χ1722222222-2-222222222222-2222222222-2-2-2-2-2-222000000-2-2-2-2-20000000000002-2-22222-2-2-2-200000000000000000000
χ1822222222-2-222222222222-2222222222-2-2-2-2-2-2-2-2000000-2-2-2-2-2000000000000-222-2-2-2-2222200000000000000000000
χ192222222-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-1-1-1-1222222-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1002200-1-1-1-10000000000
χ202222222-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-1-1-1-12222-2-211112-1-1-1-1-2-21111-2-21111222-1-1-1-1-1-1-1-100-2-20011110000000000
χ212222222-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-1-1-1-122-2-222-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-2-21111111100-2-20011110000000000
χ222222222-1222-1-1-1-12-1-12-1-122-1-1-1-12-1-1-1-1-1-1-122-2-2-2-211112-1-1-1-1-2-21111-2-21111-2-2-211111111002200-1-1-1-10000000000
χ232222222-1-2-22-1-1-1-12-1-12-1-1-22-1-1-1-12-1-1-11111-2-22200−i3i3−i3i3-2111100−i3−i3i3i300−i3−i3i3i32-2-2-1-1-1-11111000000−i3i3−i3i30000000000
χ242222222-1-2-22-1-1-1-12-1-12-1-1-22-1-1-1-12-1-1-11111-2-22200i3−i3i3−i3-2111100i3i3−i3−i300i3i3−i3−i32-2-2-1-1-1-11111000000i3−i3i3−i30000000000
χ252222222-1-2-22-1-1-1-12-1-12-1-1-22-1-1-1-12-1-1-11111-2-2-2-200−i3i3−i3i3-2111100−i3−i3i3i300−i3−i3i3i3-2221111-1-1-1-1000000i3−i3i3−i30000000000
χ262222222-1-2-22-1-1-1-12-1-12-1-1-22-1-1-1-12-1-1-11111-2-2-2-200i3−i3i3−i3-2111100i3i3−i3−i300i3i3−i3−i3-2221111-1-1-1-1000000−i3i3−i3i30000000000
χ27222222-1222-12222-122-12-12-1-1-1-1-1-1-1-1-12222-1-100222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000002200220000-1-1-1-1-1-10000
χ28222222-1222-12222-122-12-12-1-1-1-1-1-1-1-1-12222-1-100222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000-2-200-2-200001111110000
χ29222222-1222-12222-122-12-12-1-1-1-1-1-1-1-1-12222-1-100-2-2-2-2-2-2-1-1-1-1-1111111111111000000000002200-2-200001111-1-10000
χ30222222-1222-12222-122-12-12-1-1-1-1-1-1-1-1-12222-1-100-2-2-2-2-2-2-1-1-1-1-111111111111100000000000-2-200220000-1-1-1-1110000
χ312222-2-22222222-2-22-2-2222-2-222-2-2-22-2-2-2-2222222000000-2-2-222000000000000-2-2222-2-2-2-22200000000000000000000
χ322222-2-22222222-2-22-2-2222-2-222-2-2-22-2-2-2-22222-2-2000000-2-2-22200000000000022-2-2-22222-2-200000000000000000000
χ332222-2-22-1222-1-1112112-1-1-2-2-1-111-2-11111-1-12222003−3−33-211-1-10033−3−300−3−333-2-22-1-11111-1-10000003−3−330000000000
χ342222-2-22-1222-1-1112112-1-1-2-2-1-111-2-11111-1-1222200−333−3-211-1-100−3−3330033−3−3-2-22-1-11111-1-1000000−333−30000000000
χ352222-2-22-1222-1-1112112-1-1-2-2-1-111-2-11111-1-122-2-2003−3−33-211-1-10033−3−300−3−33322-211-1-1-1-111000000−333−30000000000
χ362222-2-22-1222-1-1112112-1-1-2-2-1-111-2-11111-1-122-2-200−333−3-211-1-100−3−3330033−3−322-211-1-1-1-1110000003−3−330000000000
χ372222-2-22-1-2-22-1-1112112-1-12-2-1-111-2-111-1-111-2-2222i−2i−i−iii2-1-1112i2i−i−i−i−i−2i−2iiiii-22-2-1-111-1-111002i−2i00−i−iii0000000000
χ382222-2-22-1-2-22-1-1112112-1-12-2-1-111-2-111-1-111-2-222−2i2iii−i−i2-1-111−2i−2iiiii2i2i−i−i−i−i-22-2-1-111-1-11100−2i2i00ii−i−i0000000000
χ392222-2-22-1-2-22-1-1112112-1-12-2-1-111-2-111-1-111-2-2-2-22i−2i−i−iii2-1-1112i2i−i−i−i−i−2i−2iiiii2-2211-1-111-1-100−2i2i00ii−i−i0000000000
χ402222-2-22-1-2-22-1-1112112-1-12-2-1-111-2-111-1-111-2-2-2-2−2i2iii−i−i2-1-111−2i−2iiiii2i2i−i−i−i−i2-2211-1-111-1-1002i−2i00−i−iii0000000000
χ412222-2-2-12-2-2-122-2-2-1-2-2-12-121-1-1111-11122-2-211002i−2i2i2i−2i−2i-1-1-111−i−i−i−i−i−iiiiiii000000000002-2002i−2i0000−i−iii-110000
χ422222-2-2-12-2-2-122-2-2-1-2-2-12-121-1-1111-11122-2-211002i−2i2i2i−2i−2i-1-1-111−i−i−i−i−i−iiiiiii00000000000-2200−2i2i0000ii−i−i1-10000
χ432222-2-2-12-2-2-122-2-2-1-2-2-12-121-1-1111-11122-2-21100−2i2i−2i−2i2i2i-1-1-111iiiiii−i−i−i−i−i−i000000000002-200−2i2i0000ii−i−i-110000
χ442222-2-2-12-2-2-122-2-2-1-2-2-12-121-1-1111-11122-2-21100−2i2i−2i−2i2i2i-1-1-111iiiiii−i−i−i−i−i−i00000000000-22002i−2i0000−i−iii1-10000
χ45444444-24-4-4-24444-244-24-2-4-2-2-2-2-2-2-2-2-2-4-4-4-42200000000222220000000000000000000000000000000000000000000
χ46444444-2-244-2-2-2-2-2-2-2-2-2-214-21111-2111-2-2-2-2-2-20044-2-2-2-2-21111-2-21111-2-211110000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-2-2-2-2-214-21111-2111-2-2-2-2-2-200-4-42222-2111122-1-1-1-122-1-1-1-10000000000000000000000000000000
χ48444444-2-2-4-4-2-2-2-2-2-2-2-2-2-21-4-21111-21112222220000−2i32i3−2i32i32-1-1-1-100i3i3−i3−i300i3i3−i3−i30000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-2-2-2-2-21-4-21111-211122222200002i3−2i32i3−2i32-1-1-1-100−i3−i3i3i300−i3−i3i3i30000000000000000000000000000000
χ504444-4-4-2444-244-4-4-2-4-4-24-2-42-2-2222-222-4-444-2-200000000222-2-20000000000000000000000000000000000000000000
χ514444-4-4-2-244-2-2-222-222-2-21-4211-1-121-1-122-2-2-2-2000023−23−23232-1-11100−3−3330033−3−30000000000000000000000000000000
χ524444-4-4-2-244-2-2-222-222-2-21-4211-1-121-1-122-2-2-2-20000−232323−232-1-1110033−3−300−3−3330000000000000000000000000000000
χ534444-4-4-2-2-4-4-2-2-222-222-2-214211-1-121-1-1-2-22222004i−4i−2i−2i2i2i-211-1-1−2i−2iiiii2i2i−i−i−i−i0000000000000000000000000000000
χ544444-4-4-2-2-4-4-2-2-222-222-2-214211-1-121-1-1-2-2222200−4i4i2i2i−2i−2i-211-1-12i2i−i−i−i−i−2i−2iiiii0000000000000000000000000000000
χ5544-4-44-4440044-444-4-4-4-4-440-44-4-4-44-44400000000000000000000000000000000000000000000000000000000000000
χ5644-4-44-44-2004-22-2-2-422-42-20-4-222242-2-20000000000000000000000000000000000000023−2323−2300000000000000000000
χ5744-4-44-44-2004-22-2-2-422-42-20-4-222242-2-200000000000000000000000000000000000000−2323−232300000000000000000000
χ5844-4-44-4-2400-24-4442-4-42-4-202-2222-22-2-200000000000000000000000000000000000000000000000000006−66−6000000
χ5944-4-44-4-2400-24-4442-4-42-4-202-2222-22-2-20000000000000000000000000000000000000000000000000000−66−66000000
χ6044-4-4-44440044-4-4-4-444-4-44044-444-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ6144-4-4-444-2004-2222-4-2-2-42-204-22-2-2-42220000000000000000000000000000000000000023−23−232300000000000000000000
χ6244-4-4-444-2004-2222-4-2-2-42-204-22-2-2-422200000000000000000000000000000000000000−232323−2300000000000000000000
χ6344-4-4-44-2400-24-4-4-42442-4-20-2-22-2-222220000000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ6444-4-4-44-2400-24-4-4-42442-4-20-2-22-2-222220000000000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ654-44-400444i−4i-4-4400400-4-4400-44000-400004i−4i4i−4i000000000004i−4i0000000000000000000000000000000000000000000
χ664-44-40044−4i4i-4-4400400-4-4400-44000-40000−4i4i−4i4i00000000000−4i4i0000000000000000000000000000000000000000000
χ674-44-4004-24i−4i-42-2−2i32i34−2i32i3-42-2002-2−2i32i302−2i32i323−23−2i2i4i−4i00000000023−23−2i2i0000000000000000000000000000000000000000000
χ684-44-4004-24i−4i-42-22i3−2i342i3−2i3-42-2002-22i3−2i3022i3−2i3−2323−2i2i4i−4i000000000−2323−2i2i0000000000000000000000000000000000000000000
χ694-44-4004-2−4i4i-42-2−2i32i34−2i32i3-42-2002-2−2i32i302−2i32i3−23232i−2i−4i4i000000000−23232i−2i0000000000000000000000000000000000000000000
χ704-44-4004-2−4i4i-42-22i3−2i342i3−2i3-42-2002-22i3−2i3022i3−2i323−232i−2i−4i4i00000000023−232i−2i0000000000000000000000000000000000000000000
χ714-44-400-244i−4i2-4400-2002-4-2002-2000200004i−4i−2i2i00000000000−2i2i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000000
χ724-44-400-244i−4i2-4400-2002-4-2002-2000200004i−4i−2i2i00000000000−2i2iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000000
χ734-44-400-24−4i4i2-4400-2002-4-2002-200020000−4i4i2i−2i000000000002i−2i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000000
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χ764-44-400-2-24i−4i22-2−2i32i3-2−2i32i322100-11i3−i30-1i3−i323−23−2i2i−2i2i000000000−33i−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−2ζ4−2ζ14−ζ20−ζ222ζ4+2ζ14+ζ20+ζ22ζ4+ζ14+2ζ20+2ζ22−ζ4−ζ14−2ζ20−2ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−2ζ4+2ζ14−ζ20+ζ222ζ4−2ζ14+ζ20−ζ22ζ4−ζ14+2ζ20−2ζ22−ζ4+ζ14−2ζ20+2ζ220000000000000000000000000000000
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χ784-44-400-2-24i−4i22-22i3−2i3-22i3−2i322100-11−i3i30-1−i3i3−2323−2i2i−2i2i0000000003−3i−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14+2ζ20+2ζ22−ζ4−ζ14−2ζ20−2ζ22−2ζ4−2ζ14−ζ20−ζ222ζ4+2ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14+2ζ20−2ζ22−ζ4+ζ14−2ζ20+2ζ22−2ζ4+2ζ14−ζ20+ζ222ζ4−2ζ14+ζ20−ζ220000000000000000000000000000000
χ794-44-400-2-2−4i4i22-2−2i32i3-2−2i32i322100-11i3−i30-1i3−i3−23232i−2i2i−2i0000000003−3−ii−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ222ζ4−2ζ14+ζ20−ζ22−2ζ4+2ζ14−ζ20+ζ22−ζ4+ζ14−2ζ20+2ζ22ζ4−ζ14+2ζ20−2ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ222ζ4+2ζ14+ζ20+ζ22−2ζ4−2ζ14−ζ20−ζ22−ζ4−ζ14−2ζ20−2ζ22ζ4+ζ14+2ζ20+2ζ220000000000000000000000000000000
χ804-44-400-2-2−4i4i22-2−2i32i3-2−2i32i322100-11i3−i30-1i3−i3−23232i−2i2i−2i0000000003−3−iiζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−2ζ4+2ζ14−ζ20+ζ222ζ4−2ζ14+ζ20−ζ22ζ4−ζ14+2ζ20−2ζ22−ζ4+ζ14−2ζ20+2ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−2ζ4−2ζ14−ζ20−ζ222ζ4+2ζ14+ζ20+ζ22ζ4+ζ14+2ζ20+2ζ22−ζ4−ζ14−2ζ20−2ζ220000000000000000000000000000000
χ814-44-400-2-2−4i4i22-22i3−2i3-22i3−2i322100-11−i3i30-1−i3i323−232i−2i2i−2i000000000−33−ii−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14−2ζ20+2ζ22ζ4−ζ14+2ζ20−2ζ222ζ4−2ζ14+ζ20−ζ22−2ζ4+2ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14−2ζ20−2ζ22ζ4+ζ14+2ζ20+2ζ222ζ4+2ζ14+ζ20+ζ22−2ζ4−2ζ14−ζ20−ζ220000000000000000000000000000000
χ824-44-400-2-2−4i4i22-22i3−2i3-22i3−2i322100-11−i3i30-1−i3i323−232i−2i2i−2i000000000−33−iiζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14+2ζ20−2ζ22−ζ4+ζ14−2ζ20+2ζ22−2ζ4+2ζ14−ζ20+ζ222ζ4−2ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14+2ζ20+2ζ22−ζ4−ζ14−2ζ20−2ζ22−2ζ4−2ζ14−ζ20−ζ222ζ4+2ζ14+ζ20+ζ220000000000000000000000000000000
χ834-4-44004400-4-4-400-40044400-4-40004000000004-4000000000000000000000000004-400000000000000000000000000
χ844-4-44004400-4-4-400-40044400-4-4000400000000-4400000000000000000000000000-4400000000000000000000000000
χ854-4-44004-200-422−2i32i3-42i3−2i34-2-200222i3−2i30-2−2i32i30000004-400000000000000000000000000-22−2i32i3000000000000000000000000
χ864-4-44004-200-422−2i32i3-42i3−2i34-2-200222i3−2i30-2−2i32i3000000-44000000000000000000000000002-22i3−2i3000000000000000000000000
χ874-4-44004-200-4222i3−2i3-4−2i32i34-2-20022−2i32i30-22i3−2i30000004-400000000000000000000000000-222i3−2i3000000000000000000000000
χ884-4-44004-200-4222i3−2i3-4−2i32i34-2-20022−2i32i30-22i3−2i3000000-44000000000000000000000000002-2−2i32i3000000000000000000000000
χ8988-8-88-8-4-400-4-44-4-4444442042-2-2-2-4-22200000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-4-400-4-44444-4-44420-42-2224-2-2-200000000000000000000000000000000000000000000000000000000000000
χ918-8-8800-48004-8-800400-48-40044000-40000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-4-400444−4i34i344i3−4i3-4-4200-2-2−2i32i3022i3−2i300000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-4-4004444i3−4i34−4i34i3-4-4200-2-22i3−2i302−2i32i300000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.