Finite Group DatabasebetaFinite Group Databasebeta| order | 28638 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#23750871 |
| Fitting, socle, derived | C3×C37×C43 ⋊ C2×C3 |
| Hall | C3×#18012031 ⋊ C2 |
| Hall | C37×C43 ⋊ C3×D3 |
| Sylow | C43 ⋊ C3⋊(D37⋊C3) |
| Sylow | C37 ⋊ D3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C37×C43 | C2×C3 |
| LCS | G ▷ C3×C37×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 4773 |
A minimal faithful permutation representation — 2 generators on 83 points:
(2,3)(5,9,10,6,7,11)(8,17,18,12,13,26)(14,29,30,20,21,37)(15,28,24,22,19,16)(23,39,40,32,31,35)(25,27,38,34,33,36)(42,43,45)(44,47,52)(46,50,49)(48,54,62)(51,57,59)(53,60,56)(55,64,70)(58,66,71)(61,69,68)(63,72,65)(67,76,78)(73,79,77)(74,80,75)(81,83,82);(1,2,3)(4,5,8,14,21,31,36,37,34,24,10,9,15,23,33,13,19,26,35,40,18,28,17,27,32,22,7,11,16,25,30,38,39,29,20,12,6)(41,42,44,48,55,57,43,46,51,58,67,66,47,53,61,70,78,76,54,63,73,80,62,71,64,74,81,83,72,52,59,68,77,82,79,60,45,49,56,65,75,69,50)Polycyclic presentation:
2,3^2,37,43|c^a=c^2,d^a=d^36,d^b=d^26,e^b=e^6825 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28638, 60);