Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D1171 |
| Fitting | C8×C1171 ⋊ C2 |
| derived, Sylow | C1171 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D1171 |
| commutator, hypocenter | C1171 | C2×C8 |
| Frattini | C4 | C2×D1171 |
| Fitting | C8×C1171 | C2 |
| socle | C2×C1171 | C2×C4 |
| prime radical | C2×D1171 | C4 |
| cosocle | C4×C1171 | C22 |
| LCS | G ▷ C1171 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
4696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D1171, #49153997, C2×C8×D1171, … |
| maximal normal subgroup of | C16×D1171, #49153997, C2×C8×D1171, … |
| maximal quotient of | C8×Dic1171, (C2×D1171)⋊C8, Dic1171⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 21);