Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #1020⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#1020⋊C2 |
| Fitting | C2×C3×#120 ⋊ D3 |
| derived | C22⋊A4 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1020⋊C2 |
| commutator, cosocle, hypocenter | C22⋊A4 | C23×C3 |
| Frattini | C22 | C22×C3×S4 |
| Fitting | C2×C3×#120 | D3 |
| socle | C23×C3 | C2×S4 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C2×C3 | |
945 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 945 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156667);