Finite Group Databasebeta

D61×#2087 #29709063

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD61×#2087

Splittings

FittingC61×#2087 ⋊ C2
SylowC61 ⋊ C2×#2087

Subgroups

subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2087C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2087D61
hypocenterC61C2×#2087
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2087

1054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 198618);