Finite Group DatabasebetaFinite Group Databasebeta| order | 1940 |
| isoclinism | isoclinic class of #14515595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C97 ⋊ C4 |
| Sylow | C97 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C97 | C4 |
| prime radical, cosocle | D485 | C2 |
| LCS | G ▷ C5×C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 102 |
| transitive degree | μt(G) = 485 |
Polycyclic presentation:
2^2,5,97|a^2=b,c^a=c^3,d^a=d^22,c^b=c^4,d^b=d^96125 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14515595, C7⋊#14515595, #31775610, … |
| maximal normal subgroup of | C7×#14515595, C11×#14515595, C13×#14515595, … |
| maximal quotient of | C7×#14515595, C7⋊#14515595, #31775610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1940, 8);