Finite Group Databasebeta

C2×#21447046 #29707652

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

Aliases

direct productC2×#21447046

Splittings

FittingC2×C61×#417 ⋊ C2
SylowC61 ⋊ C2×#2040

Subgroups

subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61#120
prime radicalC2×#16840340C2
hypercenterC2×#417D61
hypocenterC61C2×#2040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

1498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197207);