Finite Group DatabasebetaFinite Group Databasebeta| order | 24608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#27134395 |
| Fitting, socle | C2×C769 ⋊ C16 |
| derived, Sylow | C769 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27134395 |
| commutator, hypocenter | C769 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C769 | C16 |
| prime radical | C2×D769 | C8 |
| cosocle | #20259679 | C22 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1538 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24608, 246);