Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×#1113 |
| Fitting | C2×C33×C4 ⋊ C22 |
| derived, Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1113 |
| commutator, hypocenter | C33 | C23×C4 |
| Frattini | C2 | C22×#1113 |
| Fitting | C2×C33×C4 | C22 |
| socle | C22×C33 | C23 |
| prime radical | C22×#1113 | C2 |
| cosocle | C2×C33 | C24 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C4 | |
1122 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 231 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13155307, #13155313, #13161739, … |
| maximal normal subgroup of | #13155307, #13155313, #13161739, … |
| maximal quotient of | C4×#89040, #13178118, C4×#89041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4583);