Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C2×Q8⋊(C52⋊C3) |
| unambiguous semidirect product | (C2×Q8)⋊(C52⋊C3) |
| Fitting, Hall | C2×C52×Q8 ⋊ C3 |
| derived | C52×Q8 ⋊ C2×C3 |
| Sylow | C52 ⋊ C2×SL(2,𝔽3) |
| Sylow | C2×Q8 ⋊ C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×Q8 | C2×C3 |
| Frattini | C2 | C2×C22⋊(C52⋊C3) |
| Fitting | C2×C52×Q8 | C3 |
| socle | C22×C52 | A4 |
| LCS | G ▷ C52×Q8 | |
| UCS | C1 ◁ C22 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 883);