Finite Group Databasebeta

← Group #13135153

Character table — Group #13135153

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order12222234466666664121212123366666612121212366666666666121212121212121212121212121244448888121212121212121224242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-11-1-111-1-11-1-1111-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ61111-1-11-1-111-1-11-1-1111-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ71111-1-11-1-111-1-11-1-1111-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ81111-1-11-1-111-1-11-1-1111-1-111111111-1-1-1-11-1-1-1-111-1-1-1-111111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ92222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ102222222222222222222222-122-12-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ11222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ12222222222222222222222-12-1-12-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ132222222-2-22222222-2-2-2-2-222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000−i3i3−i3i3
χ152222222-2-22222222-2-2-2-2-22-122-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000000000000000i3−i3i3−i3
χ162222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-22222222-2-2-2-2-2-12-1-12-1221111-1-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-222222-2-22-2-2-2-2-2222222222222222-2-2-2-222-2-2-2-22-2-2-2-222-2-2-2-22222000000000000000000000000000000
χ192222-2-222222-2-22-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-211-1-11111-1-1-1-100000000000000000000000000−i3i3i3−i3
χ202222-2-222222-2-22-2-2-2-2-2222-122-12-1-12222-1-2-211-1-11111-1-2-211-1-11111-1-1-1-100000000000000000000000000i3−i3−i3i3
χ212222-2-222222-2-22-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-111-2-2221111-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i3000000
χ222222-2-222222-2-22-2-2-2-2-222-12-1-12-122-1-1-1-1-111-2-2-1-11111-111-2-2221111-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i3000000
χ232222-2-22-2-222-2-22-2-2222-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-122-1-111-1-1-1-111110000000000000000000000002-2-1-111
χ242222-2-22-2-222-2-22-2-2222-2-22-122-12-1-1-2-2-2-2-1-2-211-1-11111-122-1-111-1-1-1-11111000000000000000000000000-2211-1-1
χ252222-2-22-2-222-2-22-2-2222-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-122-2-2-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii000000
χ262222-2-22-2-222-2-22-2-2222-2-2-12-1-12-1221111-111-2-2-1-11111-1-1-122-2-2-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i000000
χ2722-2-22-22002-222-2-2-200000222-22-2-2-2000022-22-22-222-2-2-20000000000000000002−22−2000000002−22−22−22−2000000
χ2822-2-22-22002-222-2-2-200000222-22-2-2-2000022-22-22-222-2-2-2000000000000000000−22−2200000000−22−22−22−22000000
χ2922-2-22-22002-222-2-2-200000-12-1121-2-233−3−3-1-112-2-11-1-11113−3000033−3−333−3−300002−22−200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ3022-2-22-22002-222-2-2-200000-12-1121-2-233−3−3-1-112-2-11-1-11113−3000033−3−333−3−30000−22−2200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ3122-2-22-22002-222-2-2-200000-12-1121-2-2−3−333-1-112-2-11-1-1111−330000−3−333−3−33300002−22−200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ3222-2-22-22002-222-2-2-200000-12-1121-2-2−3−333-1-112-2-11-1-1111−330000−3−333−3−3330000−22−2200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ3322-2-2-222002-2-2-2-22200000222-22-2-2-200002-22-222-2-2-222-2000000000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i2000000
χ3422-2-2-222002-2-2-2-22200000222-22-2-2-200002-22-222-2-2-222-2000000000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i2000000
χ3522-2-2-222002-2-2-2-22200000-12-1121-2-233−3−3-11-1-22-1111-1-11−330000−3−33333−3−30000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ3622-2-2-222002-2-2-2-22200000-12-1121-2-233−3−3-11-1-22-1111-1-11−330000−3−33333−3−30000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ3722-2-2-222002-2-2-2-22200000-12-1121-2-2−3−333-11-1-22-1111-1-113−3000033−3−3−3−3330000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ3822-2-2-222002-2-2-2-22200000-12-1121-2-2−3−333-11-1-22-1111-1-113−3000033−3−3−3−3330000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ392-22-20022i−2i-2200-2000002i−2i22-22-2-22-22i−2i2i−2i20000-220000-200002i−2i00002i−2i2i−2i1+i−1−i1−i−1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ402-22-20022i−2i-2200-2000002i−2i22-22-2-22-22i−2i2i−2i20000-220000-200002i−2i00002i−2i2i−2i−1−i1+i−1+i1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ412-22-2002−2i2i-2200-200000−2i2i22-22-2-22-2−2i2i−2i2i20000-220000-20000−2i2i0000−2i2i−2i2i1−i−1+i1+i−1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ422-22-2002−2i2i-2200-200000−2i2i22-22-2-22-2−2i2i−2i2i20000-220000-20000−2i2i0000−2i2i−2i2i−1+i1−i−1−i1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ43444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ444444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ454444-4-444444-4-44-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-2-2-1-1-1-11111000000000000000000000000000000
χ464444-4-44-4-444-4-44-4-4444-4-4-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-2-2-2221111-1-1-1-1000000000000000000000000000000
χ4744-4-44-44004-444-4-4-4000004-24-4-2-4220000-24-4-22-22-2-222200000000000000000000000000000000000000000000
χ4844-4-44-44004-444-4-4-400000-2-2-22-22222323−23−231-22-221-111-1-1-123−230000−3−333−3−333000000000000000000000000000000
χ4944-4-44-44004-444-4-4-400000-2-2-22-2222−23−2323231-22-221-111-1-1-1−2323000033−3−333−3−3000000000000000000000000000000
χ5044-4-4-444004-4-4-4-444000004-24-4-2-4220000-2-442-2-2222-2-2200000000000000000000000000000000000000000000
χ5144-4-4-444004-4-4-4-44400000-2-2-22-22222323−23−2312-22-21-1-1-111-1−2323000033−3−3−3−333000000000000000000000000000000
χ5244-4-4-444004-4-4-4-44400000-2-2-22-2222−23−23232312-22-21-1-1-111-123−230000−3−33333−3−3000000000000000000000000000000
χ534-44-40044i−4i-4400-4000004i−4i4-2-442-4-224i−4i4i−4i-200002-2000020000−2i2i0000−2i2i−2i2i000000000000000000000000000000
χ544-44-40044i−4i-4400-4000004i−4i-242-2-424-4−2i2i−2i2i-200002-20000200004i−4i0000−2i2i−2i2i000000000000000000000000000000
χ554-44-40044i−4i-4400-4000004i−4i-2-22-222-22−2i2i−2i2i10000-113-33-3-10000−2i2i3i−3i3i−3ii−ii−i000000000000000000000000000000
χ564-44-40044i−4i-4400-4000004i−4i-2-22-222-22−2i2i−2i2i10000-11-33-33-10000−2i2i−3i3i−3i3ii−ii−i000000000000000000000000000000
χ574-44-4004−4i4i-4400-400000−4i4i4-2-442-4-22−4i4i−4i4i-200002-20000200002i−2i00002i−2i2i−2i000000000000000000000000000000
χ584-44-4004−4i4i-4400-400000−4i4i-242-2-424-42i−2i2i−2i-200002-2000020000−4i4i00002i−2i2i−2i000000000000000000000000000000
χ594-44-4004−4i4i-4400-400000−4i4i-2-22-222-222i−2i2i−2i10000-113-33-3-100002i−2i−3i3i−3i3i−ii−ii000000000000000000000000000000
χ604-44-4004−4i4i-4400-400000−4i4i-2-22-222-222i−2i2i−2i10000-11-33-33-100002i−2i3i−3i3i−3i−ii−ii000000000000000000000000000000
χ614-4-4400400-4-4004000000044-4-4-44-44000040000-4-40000400000000000000000000000000000000000000000000
χ624-4-4400400-4-400400000004-2-4-4242-20000-20000220000-200−2i32i300−2i32i32i3−2i30000000000000000000000000000000000
χ634-4-4400400-4-400400000004-2-4-4242-20000-20000220000-2002i3−2i3002i3−2i3−2i32i30000000000000000000000000000000000
χ644-4-4400400-4-40040000000-2422-4-2-44−2i32i32i3−2i3-20000220000-20000000000−2i32i32i3−2i3000000000000000000000000000000
χ654-4-4400400-4-40040000000-2422-4-2-442i3−2i3−2i32i3-20000220000-200000000002i3−2i3−2i32i3000000000000000000000000000000
χ664-4-4400400-4-40040000000-2-2222-22-2−2i32i32i3−2i310000-1-13-3-331002i3−2i300−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
χ674-4-4400400-4-40040000000-2-2222-22-2−2i32i32i3−2i310000-1-1-333-3100−2i32i300i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000
χ684-4-4400400-4-40040000000-2-2222-22-22i3−2i3−2i32i310000-1-13-3-33100−2i32i300i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ694-4-4400400-4-40040000000-2-2222-22-22i3−2i3−2i32i310000-1-1-333-31002i3−2i300−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000
χ70666666-366-3-3-3-3-3-3-36-3-3-3-30000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-100000000000000
χ71666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-2-2-200001111111100000000000000
χ72666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000000000
χ73666666-3-6-6-3-3-3-3-3-3-3-633330000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000000000
χ746666-6-6-366-3-333-333-633-3-300000000000000000000000000000000000000000000003−33−3−33−3300000000000000
χ756666-6-6-366-3-333-333-633-3-30000000000000000000000000000000000000000000000−33−333−33−300000000000000
χ766666-6-6-3-6-6-3-333-3336-3-333000000000000000000000000000000000000002i2i−2i−2i0000−i−i−i−iiiii00000000000000
χ776666-6-6-3-6-6-3-333-3336-3-33300000000000000000000000000000000000000−2i−2i2i2i0000iiii−i−i−i−i00000000000000
χ786-66-600-36i−6i3-3−3i33i33−3i33i3033−33−3i3i000000000000000000000000000000000000001+i−1−i1−i−1+i0000−ζ4+ζ14−ζ20+ζ22ζ4−ζ14ζ20−ζ22−ζ4−ζ14−ζ20−ζ22ζ4+ζ14ζ20+ζ2200000000000000
χ796-66-600-36i−6i3-3−3i33i33−3i33i3033−33−3i3i00000000000000000000000000000000000000−1−i1+i−1+i1−i0000ζ4−ζ14ζ20−ζ22−ζ4+ζ14−ζ20+ζ22ζ4+ζ14ζ20+ζ22−ζ4−ζ14−ζ20−ζ2200000000000000
χ806-66-600-36i−6i3-33i3−3i333i3−3i30−3333−3i3i000000000000000000000000000000000000001+i−1−i1−i−1+i0000−ζ20+ζ22−ζ4+ζ14ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14ζ20+ζ22ζ4+ζ1400000000000000
χ816-66-600-36i−6i3-33i3−3i333i3−3i30−3333−3i3i00000000000000000000000000000000000000−1−i1+i−1+i1−i0000ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ1400000000000000
χ826-66-600-3−6i6i3-3−3i33i33−3i33i30−33333i−3i000000000000000000000000000000000000001−i−1+i1+i−1−i0000−ζ4−ζ14−ζ20−ζ22ζ4+ζ14ζ20+ζ22−ζ4+ζ14−ζ20+ζ22ζ4−ζ14ζ20−ζ2200000000000000
χ836-66-600-3−6i6i3-3−3i33i33−3i33i30−33333i−3i00000000000000000000000000000000000000−1+i1−i−1−i1+i0000ζ4+ζ14ζ20+ζ22−ζ4−ζ14−ζ20−ζ22ζ4−ζ14ζ20−ζ22−ζ4+ζ14−ζ20+ζ2200000000000000
χ846-66-600-3−6i6i3-33i3−3i333i3−3i3033−333i−3i000000000000000000000000000000000000001−i−1+i1+i−1−i0000−ζ20−ζ22−ζ4−ζ14ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14ζ20−ζ22ζ4−ζ1400000000000000
χ856-66-600-3−6i6i3-33i3−3i333i3−3i3033−333i−3i00000000000000000000000000000000000000−1+i1−i−1−i1+i0000ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ1400000000000000
χ861212-12-1212-12-600-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000
χ871212-12-12-1212-600-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121200-60066−6i36i3-66i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-121200-600666i3−6i3-6−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000

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