Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | Q8×C37⋊C3 |
| Fitting, Hall | Q8×C37 ⋊ C3 |
| Sylow | C37 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C37⋊C3 |
| commutator, socle, cosocle | C2×C37 | C22×C3 |
| Fitting | Q8×C37 | C3 |
| prime radical | C2×C37⋊C3 | C22 |
| hypercenter | Q8 | C37⋊C3 |
| hypocenter | C37 | C3×Q8 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | #10596941⋊C3, #10596942⋊C3, SD16×C37⋊C3, … |
| maximal normal subgroup of | #10596941⋊C3, #10596942⋊C3, SD16×C37⋊C3, … |
| maximal quotient of | C4⋊C4×C37⋊C3, C2×Q8×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 24);