Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#88813 |
| derived, Sylow | C33 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1113 |
| commutator, hypocenter | C33 | C2×C42 |
| Frattini | C22 | C2×#1113 |
| Fitting, socle, prime radical | C23×C33 | C22 |
| cosocle | C22×C33 | C23 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
626 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13155043, #13155118, Dic33, … |
| maximal normal subgroup of | #13155043, #13155118, Dic33, … |
| maximal quotient of | #13161790, C2×#11722070, #13161797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3681);