Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276840 |
| Sylow | C53 ⋊ C2×#2222 |
638 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)(56,59)(57,65)(58,72)(60,78)(61,84)(62,79)(63,80)(64,86)(66,90)(67,94)(68,77)(69,91)(70,95)(71,100)(73,102)(74,106)(75,103)(76,104)(81,108)(82,111)(83,110)(85,112)(87,115)(88,107)(89,114)(92,116)(93,109)(96,118)(97,101)(98,117)(99,119)(105,113);(56,58,71,99,62,75,83,85,63,76,82,105,61,74,60,73)(57,64,81,97,68,88,93,98,69,89,92,96,67,87,66,70)(59,72,100,119,79,103,110,112,80,104,111,113,84,106,78,102)(65,86,108,101,77,107,109,117,91,114,116,118,94,115,90,95);(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)(56,57,63,69)(58,70,76,98)(59,77,80,94)(60,81,83,92)(61,68,62,67)(64,85,89,73)(65,84,91,79)(66,82,93,71)(72,101,104,118)(74,97,75,96)(78,109,110,90)(86,113,114,119)(87,105,88,99)(95,106,117,103)(100,108,111,116)(102,107,112,115);(54,55)2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324131);