Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #10596770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#10596770 |
| Fitting, socle | C25 ⋊ #157 |
| derived | A42 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10596770 |
| commutator, hypocenter | A42 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25 | #157 |
| prime radical | C2×A4⋊S4 | C2 |
| cosocle | A4⋊S4 | C22 |
| LCS | G ▷ A42 | |
| UCS | C1 ◁ C2 | |
233 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 233 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12 |
26 conjugacy classes — view the full character table.
| maximal subgroup of | #72209666, #72218849, C2×#10596770⋊C2, … |
| maximal normal subgroup of | C2×#10596770⋊C2, C22×#10596770, #72247351, … |
| maximal quotient of | #72209928, #72209932, C2×#11923442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157850);