Finite Group DatabasebetaFinite Group Databasebeta| order | 18020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C17×C53 ⋊ C4 |
| Hall | C17×C53 ⋊ Dic5 |
| Hall | C5×C53 ⋊ #595 |
| Hall | C5×C17 ⋊ #6157 |
| Sylow | C53 ⋊ #66772 |
| Sylow | C17 ⋊ #11761508 |
| Sylow | C5 ⋊ #16813357 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C53 | C4 |
| prime radical, cosocle | C5×D901 | C2 |
| LCS | G ▷ C5×C17×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4505 |
Polycyclic presentation:
2^2,5,17,53|a^2=b,c^a=c^4,d^a=d^13,e^a=e^30,d^b=d^16,e^b=e^521133 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18020, 36);