Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D111 |
| Fitting, socle | C22×C3×C37 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C23 |
| Sylow | C37 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C37 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C22 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13183839, #13183895, C2×#11725159, … |
| maximal normal subgroup of | #13183839, #13183895, C2×#11725159, … |
| maximal quotient of | C2×Dic222, C2×C4×D111, C2×D444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 60);