Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×A4×C22⋊A4 |
| Fitting, socle, Sylow | C27 ⋊ C32 |
| derived | C26 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×C22⋊A4 |
| commutator, cosocle, hypocenter | C26 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C27 | C32 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C2 | |
3924 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 3924 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4⋊#1020, C2×A4×#120⋊C3 |
| maximal normal subgroup of | C2×A4⋊#1020, C2×A4×#120⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157867);