Finite Group DatabasebetaFinite Group Databasebeta| order | 30222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C23 · Schur multiplier (H2) = C3 |
| Fitting, socle | C2×C3×C23×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C2×C32×C23 |
| Hall | C2×C23×C73 ⋊ C32 |
| Hall | C23×C73 ⋊ C2×C32 |
| Hall | C2×C73 ⋊ C32×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C2×C32×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C23×C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C3×C23 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10074 |
3726 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30222, 25);