Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×D4⋊(C3⋊(C3⋊C8)) |
| Sylow | C32 ⋊ C2×D4⋊C8 |
1032 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11777340, C2×#11777334, C2×C3⋊D3×D4⋊C8 |
| maximal normal subgroup of | C2×#11777340, C2×#11777334, C2×C3⋊D3×D4⋊C8 |
| maximal quotient of | C2×#11771603 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 8180);