Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | #125×#157 |
| Fitting | C32×#125 ⋊ C4 |
| Sylow | C32 ⋊ C4×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#157 |
| commutator, socle | C22×C32 | C23×C4 |
| Fitting | C32×#125 | C4 |
| prime radical, cosocle | C22×C3⋊D3 | C24 |
| hypercenter | #125 | #157 |
| hypocenter | C32 | C4×#125 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #125 | |
710 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36489);