Finite Group Databasebeta

C2×#21460889 #30606223

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

Aliases

direct productC2×#21460889

Splittings

SylowC61 ⋊ C2×#1385

Subgroups

subgroupG/H
centerC2×C4#14519845
commutatorC8×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC22×C16×C61C4
socleC22×C61#340
prime radicalC23×D61Q16
cosocleC2×C8×D61C23
hypercenterC22×C16#6923
hypocenterC61C2×#1385
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1095778);