Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#3828⋊C3 |
| unambiguous semidirect product | (C2×#3828)⋊C3 |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×#41 |
628 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720305, #13139931, #13139932, … |
| maximal normal subgroup of | C2×#11720305, #13139931, #13139932, … |
| maximal quotient of | C2×C4×#634⋊C3, C2×#64079⋊C3, #10595941⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2569);