Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28×C3 |
| direct product | C3⋊D3×#392 |
| Fitting | C32×#392 ⋊ C2 |
| Sylow | C32 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#392 | C2 |
| hypercenter | #392 | C3⋊D3 |
| hypocenter | C32 | C2×#392 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #392 | |
5436 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 5436 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#392, C3⋊D3×#2403, C3⋊D3×#2433, … |
| maximal normal subgroup of | C2×C3⋊D3×#392, C3⋊D3×#2403, C3⋊D3×#2433, … |
| maximal quotient of | C2×C3⋊D3×#392, C3⋊D3×#1438 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42090);