Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C22×D32×C8 |
| Fitting | C22×C32×C8 ⋊ C22 |
| derived, Sylow | C32 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D32 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C4 | C23×D32 |
| Fitting | C22×C32×C8 | C22 |
| socle | C23×C32 | C22×C4 |
| prime radical | C23×D32 | C4 |
| cosocle | C32×C4 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C8 | |
4121 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D32×#97, C2×D32×#106 |
| maximal normal subgroup of | C2×D32×#97, C2×D32×#106 |
| maximal quotient of | #72222733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152437);