Finite Group DatabasebetaFinite Group Databasebeta| order | 22340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C1117 ⋊ C4 |
| Sylow | C1117 ⋊ Dic5 |
| Sylow | C5 ⋊ #17985008 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C1117 | C4 |
| prime radical, cosocle | C5×D1117 | C2 |
| LCS | G ▷ C5×C1117 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5585 |
Polycyclic presentation:
2^2,5,1117|a^2=b,c^a=c^4,d^a=d^903,d^b=d^11161403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22340, 11);