Finite Group Databasebeta

C2×#21459617 #30587913

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#21459617

Splittings

SylowC61 ⋊ C2×#3501

Subgroups

subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#518C2
socleC23×C61C25
prime radicalC23×D4×C61C22
hypercenterC2×#518D61
hypocenterC61C2×#3501
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#518

7738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1077468);