Finite Group DatabasebetaFinite Group Databasebeta| order | 22412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D431 |
| unambiguous semidirect product | (D13×C431)⋊C2 |
| unambiguous semidirect product | (C13×D431)⋊C2 |
| unambiguous semidirect product | D5603⋊C2 |
| Fitting, socle, derived, Hall | C13×C431 ⋊ C22 |
| Sylow | C431 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D431 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C431 | C22 |
| LCS | G ▷ C13×C431 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5603 |
1736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22412, 8);