Finite Group Databasebeta

← Group #10698313

Character table — Group #10698313

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order122244442234466612121212444466121212121212444488881212121212121212121224242424242424242466121244444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-222-2-222-2-200000000-2-2000000000000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-222-2-222-2-200000000-2-20000000000000000000000-2-2220000000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-22-2-222222222-22-2-2-222-2-22200000000-2-20000000000000000000000000000002i2i−2i−2i00
χ1622222222-2-22-2-222222222-22-2-2-222-2-22200000000-2-2000000000000000000000000000000−2i−2i2i2i00
χ1722222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-200002i2i−2i−2i22000000002i2i2i2i−2i−2i−2i−2i00000000000000000000
χ1822222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000−2i−2i2i2i2200000000−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ1922222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100002i2i−2i−2i-1-13333−3−3−3−3−i−i−i−iiiii00−i3i3−i3i300000000000000
χ2022222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100002i2i−2i−2i-1-1−3−3−3−33333−i−i−i−iiiii00i3−i3i3−i300000000000000
χ2122222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111110000−2i−2i2i2i-1-13333−3−3−3−3iiii−i−i−i−i00i3−i3i3−i300000000000000
χ2222222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111110000−2i−2i2i2i-1-1−3−3−3−33333iiii−i−i−i−i00−i3i3−i3i300000000000000
χ232222-2-2-2-2222-2-2222-2-2-2-22-2-222222-2-2-2-2000000002-20000000000000000000000000022-2-2000000
χ242222-2-2-2-2222-2-2222-2-2-2-22-2-222222-2-2-2-2000000002-200000000000000000000000000-2-222000000
χ252222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22222-2-20000-2222-2-222-2-20000000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-222-2-2220000-22-2-222-2-2220000000000000000000000000000
χ272222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-200001-1-1-111-1-111−i3−i3i3i3−i3−i3i3i300−i3i3i3−i300000000000000
χ282222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-200001-1-1-111-1-111i3i3−i3−i3i3i3−i3−i300i3−i3−i3i300000000000000
χ292222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-22200001-111-1-111-1-1−i3−i3i3i3−i3−i3i3i300i3−i3−i3i300000000000000
χ302222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-22200001-111-1-111-1-1i3i3−i3−i3i3i3−i3−i300−i3i3i3−i300000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-2200000000000000002-222-2-200000000000000
χ322222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-220000000000000000-22-2-22200000000000000
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222000000002-200000000000000000000000000000000002i−2i
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22222000000002-20000000000000000000000000000000000−2i2i
χ352222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-133−3−3−3−33333−3−3−3−3332-2-1-11100000000000000
χ362222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-133−3−3−3−333−3−33333−3−3-2211-1-100000000000000
χ372222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1−3−33333−3−333−3−3−3−333-2211-1-100000000000000
χ382222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1−3−33333−3−3−3−33333−3−32-2-1-11100000000000000
χ392-2-22-2-2222-222-2-2-2222-2-200002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i200
χ402-2-22-2-2222-222-2-2-2222-2-200002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i200
χ412-2-22-2-2222-222-2-2-2222-2-200002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i200
χ422-2-22-2-2222-222-2-2-2222-2-200002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i200
χ432-2-22-2-222-222-22-2-2222-2-20000-2200-220000002−2−2200000000002−22−2−22−22000000002-200002−2−2200
χ442-2-22-2-222-222-22-2-2222-2-20000-2200-220000002−2−2200000000002−22−2−22−2200000000-220000−222−200
χ452-2-22-2-222-222-22-2-2222-2-20000-2200-22000000−222−20000000000−22−222−22−2000000002-20000−222−200
χ462-2-22-2-222-222-22-2-2222-2-20000-2200-22000000−222−20000000000−22−222−22−200000000-2200002−2−2200
χ474444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-222-2-2220000000022000000000000000000000000000000000000
χ4844444444-4-4-2-4-4-2-2-2-2-2-2-24-44-422-2-222-2-20000000022000000000000000000000000000000000000
χ494444-4-4-4-444-2-4-4-2-2-222224-4-44-2-2-2-2222200000000-22000000000000000000000000000000000000
χ504444-4-4-4-4-4-4-244-2-2-22222-4-4442222-2-2-2-200000000-22000000000000000000000000000000000000
χ5144-4-44i−4i4i−4i004004-4-44i−4i4i−4i0000000000002-22i−2i0000002-22i−2i2-22i−2i0000000000000000000000000000
χ5244-4-44i−4i4i−4i004004-4-44i−4i4i−4i000000000000-22−2i2i000000-22−2i2i-22−2i2i0000000000000000000000000000
χ5344-4-44i−4i4i−4i00-200-222−2i2i−2i2i000000−2i32i30023−232-22i−2i000000−1+31−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1−31+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000
χ5444-4-44i−4i4i−4i00-200-222−2i2i−2i2i000000−2i32i30023−23-22−2i2i0000001−3−1+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221+3−1−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000
χ5544-4-44i−4i4i−4i00-200-222−2i2i−2i2i0000002i3−2i300−23232-22i−2i000000−1−31+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1+31−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000
χ5644-4-44i−4i4i−4i00-200-222−2i2i−2i2i0000002i3−2i300−2323-22−2i2i0000001+3−1−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221−3−1+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000
χ5744-4-4−4i4i−4i4i004004-4-4−4i4i−4i4i0000000000002-2−2i2i0000002-2−2i2i2-2−2i2i0000000000000000000000000000
χ5844-4-4−4i4i−4i4i004004-4-4−4i4i−4i4i000000000000-222i−2i000000-222i−2i-222i−2i0000000000000000000000000000
χ5944-4-4−4i4i−4i4i00-200-2222i−2i2i−2i000000−2i32i300−23232-2−2i2i000000−1−31+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1+31−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000
χ6044-4-4−4i4i−4i4i00-200-2222i−2i2i−2i000000−2i32i300−2323-222i−2i0000001+3−1−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221−3−1+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000
χ6144-4-4−4i4i−4i4i00-200-2222i−2i2i−2i0000002i3−2i30023−232-2−2i2i000000−1+31−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1−31+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000
χ6244-4-4−4i4i−4i4i00-200-2222i−2i2i−2i0000002i3−2i30023−23-222i−2i0000001−3−1+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221+3−1−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000
χ634-44-44i−4i−4i4i00400-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002-22i−2i000000
χ644-44-44i−4i−4i4i00400-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000-22−2i2i000000
χ654-44-4−4i4i4i−4i00400-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002-2−2i2i000000
χ664-44-4−4i4i4i−4i00400-44-44i−4i−4i4i000000000000000000000000000000000000000000000000-222i−2i000000
χ674-4-4444-4-44-44-44-4-44-4-44400004-400-44000000000000000000000000000000000000000000000000
χ684-4-4444-4-44-4-2-4422-222-2-20000-22002-2000000000000000000006−6−666−6−6600000000000000000000
χ694-4-4444-4-44-4-2-4422-222-2-20000-22002-200000000000000000000−666−6−666−600000000000000000000
χ704-4-4444-4-4-4444-4-4-44-4-4440000-44004-4000000000000000000000000000000000000000000000000
χ714-4-4444-4-4-44-24-422-222-2-200002-200-2200000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000
χ724-4-4444-4-4-44-24-422-222-2-200002-200-2200000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000
χ734-4-44-4-4444-4-24-422-2-2-2220000-2200-22000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000
χ744-4-44-4-4444-4-24-422-2-2-2220000-2200-220000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000
χ754-4-44-4-444-44-2-4422-2-2-22200002-2002-200000022−22−22220000000000−22−222−22−200000000000000000000
χ764-4-44-4-444-44-2-4422-2-2-22200002-2002-2000000−222222−2200000000002−22−2−22−2200000000000000000000
χ778-88-88i−8i−8i8i00-4004-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i8i−8i00-4004-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000

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