Finite Group DatabasebetaFinite Group Databasebeta| order | 2704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D13×D52 |
| Fitting | C4×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D132 |
| commutator, socle, cosocle | C2×C132 | C23 |
| Fitting | C4×C132 | C22 |
| hypercenter | C4 | D132 |
| hypocenter | C132 | C2×D4 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 ◁ C4 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D132, #72259284, #72259287, … |
| maximal normal subgroup of | D4×D132, #72259284, #72259287, … |
Past the SmallGroups library coverage — no SmallGroups id.