Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215×C3 |
| direct product | C24×#638 |
| Fitting | C26×C32 ⋊ C2 |
| Sylow | C32 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C26×C32 | C2 |
| socle | C25×C32 | C22 |
| hypercenter | C26 | C3⋊D3 |
| hypocenter | C32 | C24×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C25 ◁ C26 | |
31656 conjugacy classes of subgroups; only the 6537 normal subgroups are shown.
This group has 31656 conjugacy classes of subgroups — too many to draw. Only its 6537 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153170);