Finite Group Databasebeta

C2×#21447799 #29833962

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

Aliases

direct productC2×#21447799

Splittings

FittingC2×C61×#350 ⋊ C2
SylowC61 ⋊ C2×#2195

Subgroups

subgroupG/H
centerC22#16839898
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#350C2
socleC22×C61#447
prime radicalC2×#16840579C2
hypercenterC2×#350D61
hypocenterC61C2×#2195
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1726 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323517);