Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #64188 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C22×#64188 |
| derived | C22⋊(C22⋊C9) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #64188 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊C9) | C23 |
| Frattini | C3 | C22×#1020 |
| Fitting, socle | C26×C3 | D3 |
| LCS | G ▷ C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C22 | |
2769 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 2769 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11724027, C22×#11724050, C22×C3⋊#64188, … |
| maximal normal subgroup of | C22×#11724050, A4×#64188, #72269061 |
| maximal quotient of | #72245858, C22×C3⋊#64188 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157449);