Finite Group Databasebeta

C2×#21446996 #29707451

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

Aliases

direct productC2×#21446996

Splittings

SylowC61 ⋊ C2×#2032

Subgroups

subgroupG/H
centerC22#16839674
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC22×#99×C61C2
socleC22×C61#393
prime radicalC23×D4×C61C22
hypercenterC22×#99D61
hypocenterC61C2×#2032
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1434 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, 197006);