Finite Group DatabasebetaFinite Group Databasebeta| order | 5880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#64424 |
| Fitting, socle | C22×C5×C72 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C23×C3×C5 |
| Hall | C22×C5×C7⋊D7 ⋊ C3 |
| Hall | C5×#3861 ⋊ C23 |
| Hall | C22×C7⋊D7 ⋊ C3×C5 |
| Hall | C5×C72 ⋊ C23×C3 |
| Hall | #3861 ⋊ C23×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #64424 |
| commutator, cosocle, hypocenter | C72 | C23×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C72 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C5 | |
640 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 980 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D5×#64424, C5×#72210376, #72243623 |
| maximal normal subgroup of | C22×D5×#64424, C5×#72210376, #72243623 |
Past the SmallGroups library coverage — no SmallGroups id.