Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×#3689 |
| derived | Q8⋊C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini | C2×C3 | C23×S4 |
| Fitting | C23×C3×Q8 | D3 |
| socle | C24×C3 | S4 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C24 | |
1933 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1933 conjugacy classes of subgroups — too many to draw. Only its 233 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155406);