Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C25 |
| direct product | C2×#20277009 |
| Sylow | C53 ⋊ C2×#2258 |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(58,68)(63,78)(69,88)(70,89)(71,90)(79,98)(80,99)(81,100)(91,108)(92,109)(93,110)(101,113)(102,114)(103,115)(111,118)(116,119);(56,58)(57,63)(59,69)(60,70)(61,71)(62,68)(64,79)(65,80)(66,81)(67,78)(72,91)(73,92)(74,88)(75,93)(76,89)(77,90)(82,101)(83,102)(84,98)(85,103)(86,99)(87,100)(94,111)(95,108)(96,109)(97,110)(104,116)(105,113)(106,114)(107,115)(112,118)(117,119);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(56,57,59,64,60,65,72,82,61,66,73,83,75,85,94,104,62,67,74,84,76,86,95,105,77,87,96,106,97,107,112,117)(58,63,69,79,70,80,91,101,71,81,92,102,93,103,111,116,68,78,88,98,89,99,108,113,90,100,109,114,110,115,118,119);(54,55)2240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327677);