Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C215 |
| direct product | C24×C3×#67 |
| Fitting | C26×C32 ⋊ C2 |
| Sylow | C32 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25×C3 | C2×D3 |
| commutator, cosocle | C2×C3 | C26×C3 |
| Frattini | C2 | C25×C3×D3 |
| Fitting | C26×C32 | C2 |
| socle | C25×C32 | C22 |
| hypercenter | C26×C3 | D3 |
| hypocenter | C3 | C24×C3×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C25×C3 ◁ C26×C3 | |
23929 conjugacy classes of subgroups; only the 7626 normal subgroups are shown.
This group has 23929 conjugacy classes of subgroups — too many to draw. Only its 7626 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153171);