Finite Group DatabasebetaFinite Group Databasebeta| order | 23226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×#64418 |
| Fitting, socle, Hall | C72×C79 ⋊ D3 |
| derived, Hall | #3862 ⋊ C2×C79 |
| Hall | C79×#3862 ⋊ C2 |
| Sylow | C72 ⋊ D3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | #64418 |
| commutator, cosocle, hypocenter | #3862 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C72×C79 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C79 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1106 |
1580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23226, 26);