Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#986 |
| Fitting | C2×C3×#41 ⋊ C2×D3 |
| derived | C3×SL(2,𝔽3) ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Frattini | C2 | C22×D3×S4 |
| Fitting | C2×C3×#41 | C2×D3 |
| socle | C22×C3 | C22×S4 |
| hypercenter | C2×C4 | D3×S4 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
1865 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1865 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#5429, D3×#87498, D3×#85454 |
| maximal normal subgroup of | C2×D3×#5429, D3×#87498, D3×#85454 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157603);