Finite Group DatabasebetaFinite Group Databasebeta| order | 888 |
| isoclinism | isoclinic class of D3×D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C37 ⋊ C2×C4 |
| Sylow | C37 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D37 |
| commutator, hypocenter | C3×C37 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C37 | C22 |
| prime radical | C2×D111 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
Polycyclic presentation:
2^3,3,37|a^2=c,b^2=c,e^a=e^36,d^b=d^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #13183920, #13183922, #13183964, … |
| maximal normal subgroup of | #13183920, #13183922, #13183964, … |
| maximal quotient of | #13183820, #13183823, Dic3×Dic37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(888, 17);