Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4183 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×#4183 |
| Fitting | C23×AΣL(1,𝔽27) ⋊ C2 |
| derived, Sylow | AΣL(1,𝔽27) ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #4183 |
| commutator, cosocle, hypocenter | AΣL(1,𝔽27) | C24 |
| Frattini | C32 | C23×C3⋊D3 |
| Fitting | C23×AΣL(1,𝔽27) | C2 |
| socle | C23×C3 | #272 |
| LCS | G ▷ AΣL(1,𝔽27) | |
| UCS | C1 ◁ C23 | |
1340 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#4183, C23×C3×#4183 |
| maximal normal subgroup of | C2×D4×#4183, C23×C3×#4183 |
| maximal quotient of | C2×D4×#4183, C23×C3×#4183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1917);