Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C9 |
| direct product | C2×C9⋊(C9⋊C8) |
| unambiguous semidirect product | (C2×C9)⋊(C9⋊C8) |
| derived, Sylow | C92 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C9⋊D9 |
| commutator, hypocenter | C92 | C2×C8 |
| Frattini | C32×C4 | C2×C3⋊D3 |
| Fitting | C2×C4×C92 | C2 |
| socle, prime radical | C22×C32 | C3⋊Dic3 |
| cosocle | C4×C92 | C22 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2×C4 | |
253 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1296 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×C9⋊D9, #72243951, #72244001, … |
| maximal normal subgroup of | C2×C8×C9⋊D9, #72243951, #72244001, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 481);