Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#64436 |
| derived, Hall | C3×C37 ⋊ C8 |
| Sylow | C37 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #64436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D111 |
| commutator, hypocenter | C3×C37 | C8 |
| Fitting, cosocle | C3×C4×C37 | C2 |
| socle, prime radical | C2×C3×C37 | C4 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 888 |
Polycyclic presentation:
2^3,3,37|a^2=b,b^2=c,d^a=d^2,e^a=e^36228 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×D37, D3×#64436, #13183821, … |
| maximal normal subgroup of | C3⋊C8×D37, D3×#64436, #13183821, … |
| maximal quotient of | C3⋊#10596925, C2×C3⋊#64436 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 5);