Finite Group DatabasebetaFinite Group Databasebeta| order | 2704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D13⋊#261 |
| Fitting, socle | C2×C132 ⋊ C2×C4 |
| derived, Sylow | C132 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D13⋊#261 |
| commutator, hypocenter | C132 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132 | C2×C4 |
| prime radical | C2×D132 | C2 |
| cosocle | C13⋊D13 | C23 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C2 | |
156 conjugacy classes of subgroups.
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210302, #72214198, D3×D13⋊#261, … |
| maximal normal subgroup of | C2×#72210302, #72214198, C22×D13⋊#261, … |
| maximal quotient of | #72214198, D3×D13⋊#261, C22×D13⋊#261, … |
Past the SmallGroups library coverage — no SmallGroups id.