Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×#3710 |
| derived, Sylow | C32 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D32 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C4 | C23×D32 |
| Fitting | C23×C32×C4 | C22 |
| socle | C24×C32 | C2×C4 |
| prime radical | C24×C3⋊D3 | C4 |
| cosocle | C32×C4 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C4 | |
4633 conjugacy classes of subgroups; only the 1444 normal subgroups are shown.
This group has 4633 conjugacy classes of subgroups — too many to draw. Only its 1444 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152439);