Finite Group Databasebeta

C2×#21447077 #29707800

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

Aliases

direct productC2×#21447077

Splittings

SylowC61 ⋊ C2×#2046

Subgroups

subgroupG/H
centerC23#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC23×SD16×C61C2
socleC23×C61#121
prime radicalC23×D4×C61C22
hypercenterC23×SD16D61
hypocenterC61C2×#2046
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

1458 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, 197355);