Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×C7×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C7 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C5×C7 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C5×C7 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 385 |
A minimal faithful permutation representation — 2 generators on 23 points:
(13,23,18,16,21)(14,22,19,17,20);(1,2,3,4,5)(6,7,8,9,10,11,12)(13,15,18)(14,16,20)(19,21,22)280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 573);