Finite Group DatabasebetaFinite Group Databasebeta| order | 5408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D132 |
| Fitting, socle | C23×C132 ⋊ C22 |
| derived, Sylow | C132 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D132 |
| commutator, cosocle, hypocenter | C132 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C132 | C22 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C23 | |
1898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D13⋊#261, C23×#11759815⋊C2 |
| maximal normal subgroup of | C23×D13⋊#261, C23×#11759815⋊C2 |
| maximal quotient of | #72259301 |
Past the SmallGroups library coverage — no SmallGroups id.