Finite Group Databasebeta

C2×#21445172 #29662240

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

Aliases

direct productC2×#21445172

Splittings

FittingC2×C61×#459 ⋊ C2
SylowC61 ⋊ C2×#1667

Subgroups

subgroupG/H
centerC23#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#459C2
socleC23×C61#121
hypercenterC2×#459D61
hypocenterC61C2×#1667
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 151795);