Finite Group Databasebeta

C2×#21460605 #30593861

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#21460605

Splittings

FittingC2×C61×#585 ⋊ C2
SylowC61 ⋊ C2×#3586

Subgroups

subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC4×C61C26
FrattiniC4C25×D61
FittingC2×C61×#585C2
socleC22×C61C23×D4
hypercenterC2×#585D61
hypocenterC61C2×#3586
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#585

10794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1083416);