Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2 |
| direct product | #67×C37 |
| Fitting | C22×C3×C37 ⋊ C2 |
| Hall | C3×C37 ⋊ D4 |
| Sylow | C3 ⋊ D4×C37 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C37 | C2×D3 |
| commutator, cosocle | C2×C3 | C22×C37 |
| Frattini | C2 | C2×D3×C37 |
| Fitting | C22×C3×C37 | C2 |
| socle | C2×C3×C37 | C22 |
| hypercenter | C22×C37 | D3 |
| hypocenter | C3 | D4×C37 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C37 ◁ C22×C37 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
333 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13183975, #13183977, #67×D37, … |
| maximal normal subgroup of | #13183975, #13183977, #67×D37, … |
| maximal quotient of | C37×Dic3⋊C4, C37×(C2×D3)⋊C4, C37×#213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 36);