Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #12745 |
890 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 159 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:
(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)(54,57)(55,62)(56,67)(58,77)(59,74)(60,73)(61,83)(63,89)(64,71)(65,87)(66,92)(68,97)(69,95)(70,96)(72,80)(75,102)(76,108)(78,104)(79,111)(81,101)(82,106)(84,114)(85,100)(86,90)(88,117)(91,116)(93,113)(94,98)(99,115)(103,109)(105,112)(107,110);(54,56)(55,61)(57,67)(58,76)(59,82)(60,69)(62,83)(63,88)(64,85)(65,91)(66,75)(68,79)(70,78)(71,100)(72,103)(73,95)(74,106)(77,108)(80,109)(81,84)(86,115)(87,116)(89,117)(90,99)(92,102)(93,107)(94,105)(96,104)(97,111)(98,112)(101,114)(110,113);(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)(54,55)(56,66)(57,71,73,62)(58,75)(59,81)(60,64)(61,68)(63,79)(65,78)(67,92,95,113)(69,93)(70,99)(72,102,77,110)(74,87,104,101)(76,91)(80,107)(82,88)(83,94,100,97)(84,109)(85,98)(86,105,89,111)(90,112)(96,115,106,117)(103,114,108,116)Polycyclic presentation:
2^8,53|a^2=f,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^52,d^b=dg,e^b=eh,g^b=gh,d^c=dh,f^c=fh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85275);