Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13406 |
390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 117 points:
(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)(54,57,60,78)(55,62,66,91)(56,68)(58,77,80,75)(59,83,84,111)(61,85)(63,92,65,90)(64,94,96,108)(67,97)(69,74)(70,104)(71,100)(72,102)(73,95,106,81)(76,110,112,79)(82,109)(86,99)(87,89)(88,113)(93,116)(98,117)(101,105)(103,115)(107,114);(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)(54,56)(55,61)(57,74)(58,71)(59,82)(60,72)(62,89)(63,87)(64,93)(65,67)(66,88)(68,77)(69,80)(70,84)(73,99)(75,102)(76,109)(78,100)(79,103)(81,98)(83,101)(85,90)(86,96)(91,97)(92,113)(94,117)(95,114)(104,112)(105,110)(106,116)(107,108)(111,115);(54,55)(56,67)(57,73)(58,65)(59,81)(60,66)(61,69)(62,76)(63,80)(64,79)(68,99)(70,86)(71,88)(72,87)(74,107)(75,108)(77,94)(78,106)(82,93)(83,92)(84,95)(85,104)(89,115)(90,111)(91,112)(96,110)(97,101)(98,105)(100,117)(102,116)(103,114)(109,113)Polycyclic presentation:
2^8,53|c^2=dg,d^2=h,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,c^b=cf,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eg,g^c=gh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 88902);