Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C132×C19 ⋊ C3×C4 |
| Hall | C132×Dic19 ⋊ C3 |
| Hall | #23751431 ⋊ C4 |
| Sylow | C132 ⋊ (C19⋊C3)⋊C4 |
| Hall | Dic19 ⋊ #92788 |
| Sylow | C19 ⋊ C4×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #34064232 |
| commutator, hypocenter | C132×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C132×C19 | C2×C3 |
| prime radical | C2×#23751431 | C2 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 12844 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4)(6,7,9)(8,11,14)(10,13,12)(15,17,16)(19,20,22)(21,24,27)(23,26,25)(28,30,29)(32,36,37,33,34,38)(35,43,44,39,40,48)(41,49,47,46,45,42);(18,19,21,20,23,27,24,28,30,22,25,29,26)(31,32,35,40,45,48,47,37,36,41,46,34,38,42,44,49,43,39,33);(5,6,8,7,10,14,11,15,17,9,12,16,13)Polycyclic presentation:
2,3,13^2,19,2|a^2=f,e^a=e^18,c^b=c^3,d^b=d^3,e^b=e^111250 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 119);