Finite Group Databasebeta

C2×#21460739 #30603792

order15616
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21460739

Splittings

SylowC61 ⋊ C2×#1314

Subgroups

subgroupG/H
centerC22×C4C22⋊#6923
commutatorC22×C61C22×C16
FrattiniC22×C4C22×#6923
FittingC24×C4×C61C4
socleC23×C61C22⋊C8
prime radicalC25×C61C8
cosocleC22×#92418C23
hypercenterC24×C4#6923
hypocenterC61C2×#1314
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1093347);