Finite Group Databasebeta

C2×#21447106 #29707868

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447106

Splittings

FittingC2×C61×#423 ⋊ C2
SylowC61 ⋊ C2×#2050

Subgroups

subgroupG/H
centerC2×C4#14519766
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#423C2
socleC22×C61#394
prime radicalC2×#16840562C2
hypercenterC2×#423D61
hypocenterC61C2×#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#423

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197423);