Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29 |
| direct product | C3×C4×#1004 |
| Fitting | C2×C32×C4×D4 ⋊ C2 |
| Sylow | C32 ⋊ C4×H(5,𝔽2) |
3533 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#11659463, C4×#10596675, #72227387, … |
| maximal normal subgroup of | C3×#11659463, C4×#10596675, #72227387, … |
| maximal quotient of | C3×AGL(1,𝔽5)×#1004 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134173);