Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×#1113 |
| Fitting, socle | C23×C33 ⋊ C22 |
| derived, Sylow | C33 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1113 |
| commutator, cosocle, hypocenter | C33 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C33 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
3426 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13156715, #13161931, #13167310, … |
| maximal normal subgroup of | #13156715, #13161931, #13167310, … |
| maximal quotient of | C22×#89040, C22×#89041, C2×#11724614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4719);