Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of (#1020⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×(#1020⋊C3)⋊C2 |
| unambiguous semidirect product | (#1020⋊C3)⋊C22 |
| Fitting, socle | C25 ⋊ D32 |
| derived | A42 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (#1020⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | A42 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C25 | D32 |
| LCS | G ▷ A42 | |
| UCS | C1 ◁ C2 | |
532 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157852);