Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×D7×C7⋊(C52⋊C3) |
| Fitting, socle | C3×C52×C72 ⋊ C2×C3 |
| derived, Hall | C52×C72 ⋊ C2×C32 |
| Hall | C3×C7×C7⋊(C52⋊C3) ⋊ C2 |
| Hall | C52×C7×D7 ⋊ C32 |
| Hall | C7×D7 ⋊ C3×C52⋊C3 |
| Sylow | C72 ⋊ C2×C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×C7⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C72 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 630 |
915 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 377);