Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#10596589 |
| Fitting | C2×C3×2−1+4 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C3⋊S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Frattini | C2 | C23×C3⋊S4 |
| Fitting | C2×C3×2−1+4 | D3 |
| socle | C22×C3 | C22×S4 |
| hypercenter | C2×D4 | C3⋊S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
1964 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1964 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72224794, #72258851 |
| maximal normal subgroup of | #72258851 |
| maximal quotient of | #72258851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157747);