Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3×C5 |
| direct product | D4×C3⋊D3×C5⋊D5 |
| Fitting | C32×C52×D4 ⋊ C22 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C2×D4×C3⋊D3 |
| Sylow | C32 ⋊ C2×D4×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C3⋊D3×C5⋊D5 |
| commutator, socle, cosocle | C2×C32×C52 | C24 |
| Fitting | C32×C52×D4 | C22 |
| hypercenter | D4 | C3⋊D3×C5⋊D5 |
| hypocenter | C32×C52 | C22×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C2 ◁ D4 | |
5664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×C3⋊D3×#1043, C2×D4×C3⋊D3×C5⋊D5 |
| maximal normal subgroup of | D4×C3⋊D3×#1043, C2×D4×C3⋊D3×C5⋊D5 |
| maximal quotient of | C2×D4×C3⋊D3×C5⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id.