Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C17 |
| direct product | C2×#27131466 |
| Fitting, socle | C2×C7×C172 ⋊ C2×C3 |
| derived, Hall | C7×C172 ⋊ C22×C3 |
| Hall | C2×C7⋊(C17⋊D17) ⋊ C3 |
| Hall | C7⋊(C172⋊C3) ⋊ C22 |
| Sylow | C172 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×(C17⋊D17)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27131466 |
| commutator, cosocle, hypocenter | C7×C172 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C172 | C2×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
686 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 98);