Finite Group DatabasebetaFinite Group Databasebeta| order | 1323 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×#3861 |
| Fitting, socle | C32×C72 ⋊ C3 |
| derived, Sylow | C72 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #3861 |
| commutator, cosocle, hypocenter | C72 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C32 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#64424, C3⋊D3×#3861, #72213558, … |
| maximal normal subgroup of | C32×#64424, C3⋊D3×#3861, #72213558, … |
| maximal quotient of | C2×C32×#3861, 3−1+2×#3861, C33×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1323, 49);