Finite Group DatabasebetaFinite Group Databasebeta| order | 24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C37 · Schur multiplier (H2) = C2 |
| direct product | C37×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C37 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C37 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C37 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 407 |
A minimal faithful permutation representation — 2 generators on 48 points:
(38,42,46,44,40,48,45,39,47,41,43);(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,40,43)(39,41,45)(44,46,47)296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24420, 170);