Finite Group DatabasebetaFinite Group Databasebeta| order | 23212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D829 |
| unambiguous semidirect product | (D7×C829)⋊C2 |
| unambiguous semidirect product | (C7×D829)⋊C2 |
| unambiguous semidirect product | D5803⋊C2 |
| Fitting, socle, derived, Hall | C7×C829 ⋊ C22 |
| Sylow | C829 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D829 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C829 | C22 |
| LCS | G ▷ C7×C829 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5803 |
2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23212, 8);