Finite Group Databasebeta

D61×#3293 #30556240

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD61×#3293

Splittings

FittingC61×#3293 ⋊ C2
SylowC61 ⋊ C2×#3293

Subgroups

subgroupG/H
centerC2D42×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3293C2
socleC2×C61C2×D42
hypercenter#3293D61
hypocenterC61C2×#3293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #3293

2598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1045795);