Finite Group DatabasebetaFinite Group Databasebeta| order | 30700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D307 |
| unambiguous semidirect product | C307⋊(C22×C52) |
| unambiguous semidirect product | (C2×C307)⋊(C2×C52) |
| Fitting, socle | C2×C52×C307 ⋊ C2 |
| derived, Sylow | C307 ⋊ C22×C52 |
| Hall | C52×C307 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D307 |
| commutator, cosocle, hypocenter | C307 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C307 | C2 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C2×C52 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15350 |
7750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30700, 32);