Finite Group Databasebeta

C2×#21447284 #29708956

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21447284

Splittings

SylowC61 ⋊ C2×#2082

Subgroups

subgroupG/H
centerC22#16839688
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#430C2
socleC22×C61#397
prime radicalC24×C61#41
hypercenterC2×#430D61
hypocenterC61C2×#2082
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#430

878 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, 198511);