Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #3874⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#3874⋊C2 |
| unambiguous semidirect product | #3874⋊C23 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊C23 |
| Fitting, socle | C22×C52 ⋊ C2×D3 |
| derived, Hall | C52⋊C3 ⋊ C24 |
| Sylow | C52 ⋊ C23×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #3874⋊C2 |
| commutator, cosocle, hypocenter | C52⋊C3 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52 | C2×D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C22 | |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#64480⋊C2 |
| maximal normal subgroup of | C22×#64480⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 980);