Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4174 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×#4174 |
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| derived | H(3,𝔽3) ⋊ C23×C32 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C32 | (C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C32 |
| Frattini | C32 | C22×C32×D3 |
| Fitting | C22×C3×AΣL(1,𝔽27) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C32 | |
1233 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1233 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2871);