Finite Group DatabasebetaFinite Group Databasebeta| order | 22300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C223⋊#1035 |
| Fitting, derived, Hall | C25×C223 ⋊ C4 |
| Sylow | C223 ⋊ #1035 |
| Sylow | C25 ⋊ Dic223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C223 | C4 |
| Frattini | C5 | C223⋊AGL(1,𝔽5) |
| socle | C5×C223 | AGL(1,𝔽5) |
| prime radical, cosocle | D25×C223 | C2 |
| LCS | G ▷ C25×C223 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5575 |
Polycyclic presentation:
2^2,5,223,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^222,e^a=e^2,c^b=c^4e^4,e^b=e^41564 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22300, 7);