Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C9 |
| direct product | C2×C4×C9⋊D9 |
| Fitting | C2×C4×C92 ⋊ C2 |
| derived, Sylow | C92 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C9⋊D9 |
| commutator, hypocenter | C92 | C22×C4 |
| Frattini | C2×C32 | C22×C3⋊D3 |
| Fitting | C2×C4×C92 | C2 |
| socle | C22×C32 | C2×C3⋊D3 |
| prime radical | C22×C9⋊D9 | C2 |
| cosocle | C2×C92 | C23 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2×C4 | |
621 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×#92314, C2×D4×C9⋊D9, #72219891, … |
| maximal normal subgroup of | C2×C4×#92314, C2×D4×C9⋊D9, #72219891, … |
| maximal quotient of | C42×C9⋊D9, C22⋊C4×C9⋊D9, C2×C8×C9⋊D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1132);