Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Q8⋊(C37⋊C3) |
| unambiguous semidirect product | C37⋊SL(2,𝔽3) |
| Fitting, derived, Hall | Q8×C37 ⋊ C3 |
| Sylow | C37 ⋊ SL(2,𝔽3) |
| Sylow | Q8 ⋊ C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C22⋊(C37⋊C3) |
| commutator, Fitting, cosocle, hypocenter | Q8×C37 | C3 |
| socle | C2×C37 | A4 |
| LCS | G ▷ Q8×C37 | |
| UCS | C1 ◁ C2 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
3,2^2,37,2|b^2=e,c^2=e,b^a=c,c^a=bce,d^a=d^26,c^b=ce67 conjugacy classes — view the full character table.
| maximal subgroup of | #13183942, D37⋊SL(2,𝔽3), C2×Q8⋊(C37⋊C3), … |
| maximal normal subgroup of | #13183942, D37⋊SL(2,𝔽3), C2×Q8⋊(C37⋊C3), … |
| maximal quotient of | C2×Q8⋊(C37⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 26);