Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C19 ⋊ C22×C3 |
| Hall | D13×D247 ⋊ C3 |
| Hall | #23751431 ⋊ C22 |
| Sylow | C132 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ #11759815⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C19 | C22×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 494 |
A minimal faithful permutation representation — 2 generators on 45 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(14,15,21)(16,22,26)(17,19,24)(18,25,20)(27,28,34)(29,37,44)(30,32,38)(31,41,33)(36,45,40)(39,43,42);(1,2,5,4,8,11,10,12,13,7,6,9,3)(15,16)(17,19)(18,22)(20,21)(23,25)(24,26)(28,29)(30,32)(31,35)(33,34)(36,39)(37,42)(38,43)(40,44)(41,45)Polycyclic presentation:
2^2,3,13^2,19|e^a=e^12,f^a=f^18,d^b=d^12,d^c=d^3,e^c=e^3,f^c=f^11344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 257);