Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C577 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#17987239 |
| commutator, socle | C2×C577 | C2×C8 |
| Fitting, prime radical | C22×C577 | C8 |
| cosocle | #17987237 | C22 |
| hypercenter | C22 | #17987239 |
| hypocenter | C577 | M32 |
| LCS | G ▷ C2×C577 ▷ C577 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^391,f^c=f^553,f^d=f^576308 conjugacy classes — view the full character table.
| maximal subgroup of | #49149047, #49149048, C2×#32914760, … |
| maximal normal subgroup of | #49149047, #49149048, C2×#32914760, … |
| maximal quotient of | #49149043, C22⋊#22604430, #49149052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 242);