Finite Group Databasebeta

C2×#21459707 #30588496

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#21459707

Splittings

FittingC2×C61×#551 ⋊ C2
SylowC61 ⋊ C2×#3510

Subgroups

subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#551C2
socleC23×C61C25
prime radicalC2×#16840327C2
hypercenterC2×#551D61
hypocenterC61C2×#3510
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#551

7302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1078051);