Finite Group Databasebeta

C2×#21446986 #29707413

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

Aliases

direct productC2×#21446986

Splittings

SylowC61 ⋊ C2×#2030

Subgroups

subgroupG/H
centerC23#14519745
commutator, cosocleC24×C61C24
FrattiniC24C23×D61
FittingC2×C61×#381C2
socleC23×C61#120
prime radicalC25×C61C23
hypercenterC2×#381D61
hypocenterC61C2×#2030
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#381

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 196968);