Finite Group DatabasebetaFinite Group Databasebeta| order | 18184 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C2273 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22603189 |
| commutator, hypocenter | C2273 | C8 |
| Fitting, socle, prime radical | C2×C2273 | C4 |
| cosocle | Dic2273 | C2 |
| LCS | G ▷ C2273 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18184 |
Polycyclic presentation:
2^3,2273|a^2=b,b^2=c,d^a=d^290,d^b=d^22721144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#32911534, #49138370, #49138371, … |
| maximal normal subgroup of | C2×#32911534, #49138370, #49138371, … |
| maximal quotient of | #49138365, C2×#32911534 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18184, 13);