Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C23×C5×D15 |
| Fitting, socle | C23×C3×C52 ⋊ C2 |
| derived | C3×C5 ⋊ C24×C5 |
| Hall | C3×C52 ⋊ C24 |
| Sylow | C52 ⋊ C23×D3 |
| Sylow | C3 ⋊ C23×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C52 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23×C5 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D15⋊D5 |
| maximal normal subgroup of | C23×D15⋊D5 |
| maximal quotient of | C5×#92095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 1038);