Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#6294 |
| derived, Sylow | C33 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1113 |
| commutator, hypocenter | C33 | C23×C4 |
| Frattini | C2 | C22×#1113 |
| Fitting, socle | C23×C33 | C22 |
| prime radical | C23×C3×C3⋊D3 | C2 |
| cosocle | C2×C33 | C24 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C23 | |
1218 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 303 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 | #13156688, #13156699, #13156724, … |
| maximal normal subgroup of | #13156688, #13156699, #13156724, … |
| maximal quotient of | C2×#11723668, #13178491, C2×#11723673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4595);