Finite Group Databasebeta

D61×#1603 #29652106

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

Aliases

direct productD61×#1603

Splittings

FittingC61×#1603 ⋊ C2
SylowC61 ⋊ C2×#1603

Subgroups

subgroupG/H
centerC22#120×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1603C2
socleC22×C61C2×#120
prime radical#121×D61C22
hypercenter#1603D61
hypocenterC61C2×#1603
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1603

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 141661);