Finite Group DatabasebetaFinite Group Databasebeta| order | 18136 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C2267⋊C8 |
| derived, Sylow | C2267 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D2267 |
| commutator, hypocenter | C2267 | C8 |
| Fitting, cosocle | C4×C2267 | C2 |
| socle, prime radical | C2×C2267 | C4 |
| LCS | G ▷ C2267 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18136 |
Polycyclic presentation:
2^3,2267|a^2=b,b^2=c,d^a=d^22664540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D2267, C2×C2267⋊C8, #49136720, … |
| maximal normal subgroup of | C8×D2267, C2×C2267⋊C8, #49136720, … |
| maximal quotient of | C2267⋊C16, C2×C2267⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18136, 6);