Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88587 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88589 |
| Sylow | H(3,𝔽3) ⋊ C2×Q16 |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | #13146181, #13146573, #13146579, … |
| maximal normal subgroup of | #13146181, #13146573, #13146579, … |
| maximal quotient of | #13146512, #13146524, #13146528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2278);