Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#72985 |
| Fitting | C2×C3×#95 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×#857 |
| commutator, cosocle, hypocenter | #95⋊C3 | C22×C3 |
| Frattini | C23 | C2×C3×S4 |
| Fitting | C2×C3×#95 | D3 |
| socle | C23×C3 | C2×S4 |
| hypercenter | C22×C3 | #857 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3 | |
286 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72209884, C2×C3×#72985 |
| maximal normal subgroup of | C2×C3×#72985 |
| maximal quotient of | C2×C3×#72985 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154774);