Finite Group Databasebeta

D61×#1501 #29647103

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD61×#1501

Splittings

FittingC61×#1501 ⋊ C2
SylowC61 ⋊ C2×#1501

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1501C2
socleC22×C61C22×C22⋊C4
prime radical#525×D61C2
cosocleC22×C4×C61C24
hypercenter#1501D61
hypocenterC61C2×#1501
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

1606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 136658);