Finite Group Databasebeta

C2×#21444793 #29652197

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

Aliases

direct productC2×#21444793

Splittings

SylowC61 ⋊ C2×#1605

Subgroups

subgroupG/H
centerC23#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#544C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#544D61
hypocenterC61C2×#1605
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 141752);