Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3×C11 |
| direct product | C3×C7×C22⋊(C112⋊C3) |
| unambiguous semidirect product | (C22×C3)⋊(C7×C112⋊C3) |
| unambiguous semidirect product | (C3×C112)⋊(C7×A4) |
| Fitting, socle | C22×C3×C7×C112 ⋊ C3 |
| derived, Hall | C22×C112 ⋊ C32×C7 |
| Hall | C22×C7×C112 ⋊ C32 |
| Hall | C7×C112 ⋊ C3×A4 |
| Sylow | C112 ⋊ C3×C7×A4 |
| Hall | C22×C7 ⋊ C3×C112⋊C3 |
| Sylow | C22 ⋊ C3×C7×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C22⋊(C112⋊C3) |
| commutator, cosocle, hypocenter | C22×C112 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C7×C112 | C3 |
| LCS | G ▷ C22×C112 | |
| UCS | C1 ◁ C3×C7 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
3444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 473);