Finite Group Databasebeta

C2×#21447784 #29833953

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

Aliases

direct productC2×#21447784

Splittings

FittingC2×C61×#359 ⋊ C2
SylowC61 ⋊ C2×#2193

Subgroups

subgroupG/H
centerC22#16839897
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#359C2
socleC22×C61#447
hypercenterC2×#359D61
hypocenterC61C2×#2193
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323508);