Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C7 |
| direct product | D5×C31×C7⋊D7 |
| unambiguous semidirect product | (C7×D5)⋊(D7×C31) |
| Fitting, socle, Hall | C5×C72×C31 ⋊ C22 |
| derived, Hall | C5×C72 ⋊ C22×C31 |
| Hall | C72×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D5×C31 |
| Sylow | C5 ⋊ C2×C31×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D5×C7⋊D7 |
| commutator, cosocle, hypocenter | C5×C72 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C31 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C31 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
3224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 100);