Finite Group Databasebeta

C2×D61⋊#365 #30624114

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×D61⋊#365
unambiguous semidirect productD61⋊(C2×#365)

Splittings

FittingC2×M32×C61 ⋊ C4
SylowC61 ⋊ C22×#365

Subgroups

subgroupG/H
centerC22C2×#14519845
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC2×M32×C61C4
socleC22×C61C2×#106
prime radicalC23×D61SD16
cosocleC8×D61C24
hypercenterC2×M32#6923
hypocenterC61C22×#365
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113669);