Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C72 · Schur multiplier (H2) = C3×C5×C7 |
| direct product | C3×C72×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5)⋊(C32×C72) |
| unambiguous semidirect product | (C3×C5⋊D5)⋊(C3×C72) |
| Fitting, socle | C3×C52×C72 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C2×C32×C72 |
| Hall | C3×C72×C52⋊C3 ⋊ C2 |
| Hall | C72×C5⋊D5 ⋊ C32 |
| Hall | C52×C72 ⋊ C2×C32 |
| Hall | C3×C52⋊C3 ⋊ C2×C72 |
| Hall | C5⋊D5 ⋊ C32×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C32×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C72 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
1470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 384);