Finite Group DatabasebetaFinite Group Databasebeta| order | 24278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C199 · Schur multiplier (H2) = C1 |
| direct product | D61×C199 |
| unambiguous semidirect product | C61⋊(C2×C199) |
| Fitting, socle, Hall | C61×C199 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C199 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C199 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C199 |
| Frattini | C1 | G |
| Fitting, socle | C61×C199 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C199 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12139 |
6368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24278, 1);