Finite Group DatabasebetaFinite Group Databasebeta| order | 18184 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2273 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2273 | C8 |
| prime radical | D2273 | C4 |
| cosocle | #22603189 | C2 |
| LCS | G ▷ C2273 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2273 |
Polycyclic presentation:
2^3,2273|a^2=b,b^2=c,d^a=d^1808,d^b=d^290,d^c=d^2272292 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#32911536, #49138376 |
| maximal normal subgroup of | C2×#32911536, #49138376 |
| maximal quotient of | #49138374, C2×#32911536 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18184, 15);