Finite Group Databasebeta

C2×#21447091 #29707842

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

Aliases

direct productC2×#21447091

Splittings

FittingC22×#100×C61 ⋊ C2
SylowC61 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#16839678
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#100×C61C2
socleC22×C61#394
prime radicalC22×#14519803C2
hypercenterC22×#100D61
hypocenterC61C2×#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197397);