Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#63568 |
| Sylow | C32 ⋊ C4×#104 |
849 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10590393, C4×#10591510, C4×#10591522, … |
| maximal normal subgroup of | C4×#10590393, C4×#10591510, C4×#10591522 |
| maximal quotient of | AGL(1,𝔽5)×#63568 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17891);