Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#10597048 |
| Fitting | C23×C3×C25 ⋊ C2 |
| Hall | C3×C25 ⋊ C2×D4 |
| Sylow | C25 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×C22⋊D25 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D75 |
| commutator, cosocle | C2×C3×C25 | C23 |
| Frattini | C2×C5 | C22×D15 |
| Fitting | C23×C3×C25 | C2 |
| socle | C22×C3×C5 | C2×D5 |
| hypercenter | C23 | D75 |
| hypocenter | C3×C25 | C2×D4 |
| LCS | G ▷ C2×C3×C25 ▷ C3×C25 | |
| UCS | C1 ◁ C22 ◁ C23 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 178);