Finite Group DatabasebetaFinite Group Databasebeta| order | 33222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C49⋊C3×D113 |
| unambiguous semidirect product | C113⋊(C2×C49⋊C3) |
| unambiguous semidirect product | (C49×D113)⋊C3 |
| Fitting, derived, Hall | C49×C113 ⋊ C2×C3 |
| Hall | C113×C49⋊C3 ⋊ C2 |
| Hall | C49×D113 ⋊ C3 |
| Sylow | C113 ⋊ C2×C49⋊C3 |
| Sylow | C49 ⋊ C3×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C113 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×D113 |
| socle | C7×C113 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C49×C113 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5537 |
1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33222, 14);