Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C23×C3⋊(C5⋊D5) |
| Fitting, socle | C23×C3×C52 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C24 |
| Sylow | C52 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C52 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C23 | |
1072 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1039);