Finite Group DatabasebetaFinite Group Databasebeta| order | 5512 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C22×D53⋊C13 |
| Fitting, socle | C22×C53 ⋊ C2×C13 |
| derived, Sylow | C53 ⋊ C23×C13 |
| Hall | C53⋊C13 ⋊ C23 |
| Hall | C22×D53 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D53⋊C13 |
| commutator, cosocle, hypocenter | C53 | C23×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C2×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 212 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽53), D4×D53⋊C13, #72275969 |
| maximal normal subgroup of | C22×AGL(1,𝔽53), D4×D53⋊C13, #72275969 |
| maximal quotient of | D4×D53⋊C13 |
Past the SmallGroups library coverage — no SmallGroups id.