Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C37⋊C3)⋊Q8 |
| unambiguous semidirect product | Dic74⋊C3 |
| Hall | Dic74 ⋊ C3 |
| Hall | C37⋊C3 ⋊ Q8 |
| Sylow | C37 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D37⋊C3 |
| commutator, socle, cosocle | C2×C37 | C22×C3 |
| Fitting | C4×C37 | C2×C3 |
| prime radical | C2×C37⋊C3 | C22 |
| hypercenter | C4 | D37⋊C3 |
| hypocenter | C37 | C3×Q8 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^2,3,2,37|a^2=d,b^2=d,b^a=bd,e^a=e^36,e^c=e^2639 conjugacy classes — view the full character table.
| maximal subgroup of | #10596930⋊C3, Dic148⋊C3, #10596940⋊C3, … |
| maximal normal subgroup of | #10596930⋊C3, Dic148⋊C3, #10596940⋊C3, … |
| maximal quotient of | #10596936⋊C3, C4⋊(Dic37⋊C3), C2×(C37⋊C3)⋊Q8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 8);