Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D4×C3⋊GL(2,𝔽3) |
| Fitting | C3×D4×Q8 ⋊ D3 |
1056 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SO+(4,𝔽3), #72258851, D3×D4×GL(2,𝔽3), … |
| maximal normal subgroup of | #72258851, D3×D4×GL(2,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156957);