Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C5 |
| direct product | C23×(C5⋊D5)⋊C3 |
| Fitting, socle | C23×C52 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C24×C3 |
| Hall | C23×C5⋊D5 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C5⋊D5)⋊C3 |
| commutator, cosocle, hypocenter | C52 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1012);