Finite Group Databasebeta

C2×D61⋊#410 #30625158

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×D61⋊#410
unambiguous semidirect productD61⋊(C2×#410)

Splittings

FittingC22×#41×C61 ⋊ C4
SylowC61 ⋊ C22×#410

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC22×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#41×D61C2
cosocleC22×D61C25
hypercenterC22×#41#6923
hypocenterC61C22×#410
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

5278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114713);