Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×#72231393 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C2×#3811 |
| Sylow | C32 ⋊ C22×C22⋊(C5⋊D5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×C5⋊D5 |
| commutator, cosocle | C2×C32×C52 | C24 |
| Frattini | C2 | C2×D32×C5⋊D5 |
| Fitting, socle | C22×C32×C52 | C23 |
| hypocenter | C32×C52 | C22×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
4312 conjugacy classes of subgroups; only the 460 normal subgroups are shown.
This group has 4312 conjugacy classes of subgroups — too many to draw. Only its 460 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 600 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊D5×#3811 |
| maximal normal subgroup of | C2×C5⋊D5×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.