Finite Group DatabasebetaFinite Group Databasebeta| order | 24442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C101 · Schur multiplier (H2) = C1 |
| direct product | C11×D11×C101 |
| unambiguous semidirect product | C11⋊(C2×C11×C101) |
| Fitting, socle, Hall | C112×C101 ⋊ C2 |
| derived | C11 ⋊ C2×C11×C101 |
| Sylow | C112 ⋊ C2×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C101 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C11×C101 |
| Frattini | C1 | G |
| Fitting, socle | C112×C101 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C101 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2222 |
7777 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24442, 7);