Finite Group DatabasebetaFinite Group Databasebeta| order | 30268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C23 · Schur multiplier (H2) = C2 |
| direct product | C22×C7×C47⋊C23 |
| unambiguous semidirect product | (C22×C47)⋊(C7×C23) |
| unambiguous semidirect product | (C22×C7×C47)⋊C23 |
| Fitting, socle, Hall | C22×C7×C47 ⋊ C23 |
| derived, Sylow | C47 ⋊ C22×C7×C23 |
| Hall | C7×C47 ⋊ C22×C23 |
| Hall | C22×C47 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | C47⋊C23 |
| commutator, cosocle, hypocenter | C47 | C22×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C22×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1316 |
700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30268, 18);