Finite Group DatabasebetaFinite Group Databasebeta| order | 30268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C7⋊AGL(1,𝔽47) |
| unambiguous semidirect product | (C2×C7)⋊AGL(1,𝔽47) |
| unambiguous semidirect product | (C2×D329)⋊C23 |
| unambiguous semidirect product | (C2×C47⋊C23)⋊D7 |
| Fitting, socle | C2×C7×C47 ⋊ C2×C23 |
| derived, Hall | C7×C47 ⋊ C22×C23 |
| Hall | C7×C47⋊C23 ⋊ C22 |
| Hall | C2×D329 ⋊ C23 |
| Hall | C47⋊C23 ⋊ C2×D7 |
| Sylow | C47 ⋊ C2×D7×C23 |
| Sylow | C7 ⋊ C2×AGL(1,𝔽47) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊AGL(1,𝔽47) |
| commutator, cosocle, hypocenter | C7×C47 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C47 | C2×C23 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 658 |
244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30268, 16);