Finite Group Databasebeta

C2×#21443695 #29569976

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21443695

Splittings

SylowC61 ⋊ C2×#1293

Subgroups

subgroupG/H
centerC23#14519684
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#407C2
socleC23×C61#95
prime radicalC25×C61Q8
cosocleC23×C4×C61C23
hypercenterC2×#407D61
hypocenterC61C2×#1293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59531);