Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C4 |
| direct product | SL(2,𝔽3)×C42⋊C3 |
| unambiguous semidirect product | (Q8×C42⋊C3)⋊C3 |
| unambiguous semidirect product | (C42×SL(2,𝔽3))⋊C3 |
| unambiguous semidirect product | #73284⋊C3 |
| Fitting, derived, Sylow | C42×Q8 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×C42⋊C3 |
| commutator, Fitting, cosocle, hypocenter | C42×Q8 | C32 |
| Frattini, socle | C23 | A42 |
| LCS | G ▷ C42×Q8 | |
| UCS | C1 ◁ C2 | |
136 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154765);