Finite Group DatabasebetaFinite Group Databasebeta| order | 22700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C227⋊#1039 |
| derived, Hall | C52×C227 ⋊ C4 |
| Sylow | C227 ⋊ #1039 |
| Sylow | C52 ⋊ Dic227 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊D1135 |
| commutator, hypocenter | C52×C227 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C52×C227 | C2 |
| LCS | G ▷ C52×C227 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22700 |
Polycyclic presentation:
2,5^2,227,2|a^2=e,b^a=b^4,c^a=c^4,d^a=d^2265678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22700, 13);