Finite Group DatabasebetaFinite Group Databasebeta| order | 5408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C13 |
| direct product | C23×#10621729 |
| Fitting, socle | C23×C132 ⋊ C4 |
| derived, Sylow | C132 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10621729 |
| commutator, hypocenter | C132 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C132 | C4 |
| prime radical | C23×C13⋊D13 | C2 |
| cosocle | C13⋊D13 | C24 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C23 | |
874 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D13⋊#261 |
| maximal normal subgroup of | C23×D13⋊#261 |
| maximal quotient of | #72259332 |
Past the SmallGroups library coverage — no SmallGroups id.