Finite Group Databasebeta

D61×#2050 #29707864

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD61×#2050

Splittings

FittingC61×#2050 ⋊ C2
SylowC61 ⋊ C2×#2050

Subgroups

subgroupG/H
centerC4#124×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2050C2
socleC2×C61C2×#394
prime radical#575×D61C2
hypercenter#2050D61
hypocenterC61C2×#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2050

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197419);