Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C37 ⋊ D4 |
| Sylow | C37 ⋊ #67 |
| Sylow | C3 ⋊ C22⋊D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D37 |
| commutator, Fitting, socle, cosocle | C2×C3×C37 | C22 |
| hypocenter | C3×C37 | D4 |
| LCS | G ▷ C2×C3×C37 ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 444 |
Polycyclic presentation:
2^3,3,37|b^a=bc,e^a=e^36,d^b=d^2117 conjugacy classes — view the full character table.
| maximal subgroup of | #13183960, #13183966, #13183967, … |
| maximal normal subgroup of | #13183960, #13183966, #13183967, … |
| maximal quotient of | #13183824, #13183827, #13183828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 18);