Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#1020 |
| Fitting, socle | C25×C3 ⋊ C2×D3 |
| derived | C3×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#1020 |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C25×C3 | C2×D3 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
2881 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 2881 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11715753, C22×D3×#1020, C2×D3×A4⋊S4, … |
| maximal normal subgroup of | C22×D3×#1020, C2×D3×#1020⋊C2, D3×#87524, … |
| maximal quotient of | D3×#11715753, C2×D3×#5935, D3×#87520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157864);