Finite Group DatabasebetaFinite Group Databasebeta| order | 22698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21438966 |
| Fitting, socle, derived | C3×C13×C97 ⋊ C2×C3 |
| Hall | C3×#16838253 ⋊ C2 |
| Hall | C13×C97 ⋊ C3×D3 |
| Sylow | C97 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ D3×C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C97 | C2×C3 |
| LCS | G ▷ C3×C13×C97 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 3783 |
A minimal faithful permutation representation — 2 generators on 113 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,68)(41,55,66)(44,58,63)(47,61,60)(50,64,57)(52,67,54)(56,71,81)(59,72,80)(62,75,77)(65,78,74)(69,82,70)(73,83,90)(76,84,89)(79,87,86)(85,91,95)(88,92,94)(93,96,97)(99,103,104,100,101,105)(102,109,108,106,107,110)(112,113);(1,2,4,8,15,25,38,49,22,32,45,60,74,71,37,52,68,81,90,95,97,96,84,58,27,7,13,21,31,44,59,73,78,46,20,5,9,16,26,39,54,70,67,35,48,63,77,86,83,55,24,36,50,65,79,88,93,92,75,43,17,3,6,11,18,28,41,56,64,33,12,19,29,42,57,53,69,82,51,66,80,89,94,91,72,40,14,23,34,47,62,76,85,87,61,30,10)(98,99,102,101,105,108,107,109,110,104,103,106,100)(111,112,113)Polycyclic presentation:
2,3^2,13,97|c^a=c^2,d^a=d^12,d^b=d^3,e^b=e^61687 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22698, 48);