Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4×#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C24 |
| direct product | A4×#1020 |
| Fitting, socle | C26 ⋊ C3×D3 |
| derived | C22×C22⋊A4 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C22⋊A4 | C2×C3 |
| Fitting, socle | C26 | C3×D3 |
| LCS | G ▷ C22×C22⋊A4 | |
| UCS | C1 | |
693 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 693 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | A4×A4⋊S4, S4×#1020, C22⋊A4×#1020, … |
| maximal normal subgroup of | S4×#1020, A4×#1020⋊C2, #72241489, … |
| maximal quotient of | C22⋊A4×#1020, SL(2,𝔽3)×#1020, A4×#5934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157855);