Finite Group Databasebeta

C2×#21447846 #29834183

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

Aliases

direct productC2×#21447846

Splittings

FittingC2×C61×#355 ⋊ C2
SylowC61 ⋊ C2×#2204

Subgroups

subgroupG/H
centerC22#16839950
commutator, cosocleC2×Q8×C61C24
FrattiniC2×Q8C23×D61
FittingC2×C61×#355C2
socleC22×C61B(4,𝔽2)
hypercenterC2×#355D61
hypocenterC61C2×#2204
LCSG ▷ C2×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323738);