Finite Group DatabasebetaFinite Group Databasebeta| order | 37380 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C89 · Schur multiplier (H2) = C2 |
| direct product | C7×A5×C89 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C7×C89 | A5 |
| commutator, hypocenter | A5 | C7×C89 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C7×C89 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3115 |
A minimal faithful permutation representation — 2 generators on 101 points:
(1,2,3,4,5)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2,5,3,4)(6,7,8,9,10,11,12)3115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37380, 129);