Finite Group Databasebeta

D61×#2090 #29709126

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

Aliases

direct productD61×#2090

Splittings

FittingC61×#2090 ⋊ C2
SylowC61 ⋊ C2×#2090

Subgroups

subgroupG/H
centerC22#121×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2090C2
socleC22×C61C2×#121
prime radicalC23×D61#41
hypercenter#2090D61
hypocenterC61C2×#2090
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2090

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 198681);