Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×#611 |
| Fitting | C26×C9 ⋊ C2 |
| Sylow | C9 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini | C2×C3 | C25×D3 |
| Fitting | C26×C9 | C2 |
| socle | C25×C3 | C2×D3 |
| hypercenter | C26 | D9 |
| hypocenter | C9 | C24×D4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C25 ◁ C26 | |
15828 conjugacy classes of subgroups; only the 4494 normal subgroups are shown.
This group has 15828 conjugacy classes of subgroups — too many to draw. Only its 4494 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, 153169);