Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×#72215767 |
| Fitting | C2×#63103 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#1020 |
| commutator, cosocle, hypocenter | #997 | C25 |
| Frattini | C2 | C24×#1020 |
| Fitting | C2×#63103 | D3 |
| socle | C22 | C23×#1020 |
| hypercenter | C2×#41 | #1020 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Only the 712 normal subgroups are shown; non-normal subgroups are omitted.
172 conjugacy classes — view the full character table.
| maximal subgroup of | #72341591, C2×#72236955, #72341901, … |
| maximal normal subgroup of | #72341591, C2×#72236955, #72341901, … |
Past the SmallGroups library coverage — no SmallGroups id.