Finite Group DatabasebetaFinite Group Databasebeta| order | 24444 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C97 ⋊ C32×C4 |
| Hall | ΓL(1,𝔽8)×C97⋊C3 ⋊ C4 |
| Hall | C7×#87604 ⋊ C32 |
| Hall | #87604 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C97 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×#87604⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C97 | C32×C4 |
| prime radical | ΓL(1,𝔽8)×D97⋊C3 | C2 |
| cosocle | C7×D97 | C2×C32 |
| LCS | G ▷ C7×C97 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 679 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24444, 128);