Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C3×C43 |
| direct product | C2×C42×#157 |
| Fitting | C2×C32×C42 ⋊ C4 |
| derived, Sylow | C32 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #157 |
| commutator, hypocenter | C32 | C2×C43 |
| Frattini | C22 | C23×#157 |
| Fitting | C2×C32×C42 | C4 |
| socle | C23×C32 | C22×C4 |
| prime radical | C23×C3⋊D3 | C23 |
| cosocle | C22×C3⋊D3 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C42 | |
1770 conjugacy classes of subgroups; only the 690 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 690 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34657);