Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #33974 |
462 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 391 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 — 4 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)(55,62)(61,76)(63,80)(64,81)(65,82)(77,96)(78,97)(79,98)(83,102)(84,103)(85,104)(99,111)(100,112)(101,113)(105,115)(114,117);(56,66)(61,76)(67,86)(68,87)(69,88)(77,96)(78,97)(79,98)(89,106)(90,107)(91,108)(99,111)(100,112)(101,113)(109,116)(114,117);(54,56)(55,61)(57,67)(58,68)(59,69)(60,66)(62,76)(63,77)(64,78)(65,79)(70,89)(71,90)(72,86)(73,91)(74,87)(75,88)(80,96)(81,97)(82,98)(83,99)(84,100)(85,101)(92,109)(93,106)(94,107)(95,108)(102,111)(103,112)(104,113)(105,114)(110,116)(115,117);(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)(54,55,57,63,58,64,70,83,59,65,71,84,73,85,92,105,60,62,72,80,74,81,93,102,75,82,94,103,95,104,110,115)(56,61,67,77,68,78,89,99,69,79,90,100,91,101,109,114,66,76,86,96,87,97,106,111,88,98,107,112,108,113,116,117)Polycyclic presentation:
2^8,53|a^2=e,e^2=f,f^2=g,g^2=h,d^a=dh,i^a=i^52,c^b=ch2216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 327681);