Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C23×C3×C4 |
| direct product | C3×#2679⋊C3 |
| unambiguous semidirect product | #2679⋊C32 |
| unambiguous semidirect product | (C3×#2679)⋊C3 |
| Fitting | C3×#2679 ⋊ C3 |
| derived, Sylow | #2679 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #5464 |
| commutator, cosocle, hypocenter | #2679 | C32 |
| Frattini | C23 | C3×C22⋊A4 |
| Fitting | C3×#2679 | C3 |
| socle | C23×C3 | C22⋊A4 |
| LCS | G ▷ #2679 | |
| UCS | C1 ◁ C2×C3 | |
488 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14515300, C3×#11714279, C2×C3×#2679⋊C3 |
| maximal normal subgroup of | C3×#11714279, C2×C3×#2679⋊C3 |
| maximal quotient of | C3×#11709313, C2×C3×#2679⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153655);