Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | A4×#1004 |
| unambiguous semidirect product | (C22×#1004)⋊C3 |
| Fitting | C23×C3×D4 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D3×A4 |
| commutator, socle, cosocle | C23×C3 | C24×C3 |
| Fitting | C23×C3×D4 | C2×C3 |
| hypercenter | C2×D4 | D3×A4 |
| hypocenter | C22×C3 | C3×H(5,𝔽2) |
| LCS | G ▷ C23×C3 ▷ C22×C3 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
2794 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 2794 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #72259031, A4×#87477 |
| maximal normal subgroup of | #72259031 |
| maximal quotient of | A4×#87477 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157807);