Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×#11710937 |
| Fitting, Sylow | C2×#63103 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×C22⋊A4 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C24×C3 |
| Frattini | C2 | C24×C22⋊A4 |
| Fitting | C2×#63103 | C3 |
| socle | C22 | C23×C22⋊A4 |
| hypercenter | C2×#41 | C22⋊A4 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Only the 539 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 539 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72227619, C2×#72218407, C2×#72233470, … |
| maximal normal subgroup of | C2×#72227619, C2×#72233470, #72271662, … |
Past the SmallGroups library coverage — no SmallGroups id.