Finite Group DatabasebetaFinite Group Databasebeta| order | 38220 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C13 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×C13×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C72×C13 | A5 |
| commutator, hypocenter | A5 | C72×C13 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C72×C13 | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 3185 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,4,3,5,2)(6,7,8,9,10,11,12)(13,14,16,18,15,17,19);(1,2,3,4,5)(13,15,14,17,16,19,18)(20,21,22,23,24,25,26,27,28,29,30,31,32)3185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38220, 1220);