Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6295 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#6295 |
| Sylow | C33 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #1113 |
| commutator | C2×C33 | C22×C4 |
| Frattini | C22 | C2×#1113 |
| Fitting | C2×C33×C4 | C22 |
| socle, cosocle | C22×C33 | C23 |
| prime radical | C2×#6295 | C2 |
| hypocenter | C33 | C4×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C4 | |
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #13154962, #13155073, #13155555, … |
| maximal normal subgroup of | #13154962, #13155073, #13155555, … |
| maximal quotient of | C4×#88810, #13161511, C4×#88811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3660);