Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#29503118 |
| Fitting, socle | C2×C7×C192 ⋊ C2×C3 |
| derived, Hall | C7×C192 ⋊ C22×C3 |
| Hall | C2×C19×D133 ⋊ C3 |
| Hall | C19×#87705 ⋊ C22 |
| Sylow | C192 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×D19×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #29503118 |
| commutator, cosocle, hypocenter | C7×C192 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C192 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1596 |
920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 225);