Finite Group DatabasebetaFinite Group Databasebeta| order | 22220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C101 ⋊ C4×C5 |
| Hall | #19149921 ⋊ C4 |
| Hall | Dic1111 ⋊ C5 |
| Sylow | C101 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ Dic101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26013202 |
| commutator, hypocenter | C11×C101 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C101 | C2×C5 |
| prime radical | C2×#19149921 | C2 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4444 |
Polycyclic presentation:
2,5,11,101,2|a^2=e,c^a=c^10,d^a=d^100,c^b=c^4,d^b=d^95242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22220, 29);