Finite Group Databasebeta

C2×#21462134 #30624058

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21462134

Splittings

SylowC61 ⋊ C2×#2143

Subgroups

subgroupG/H
centerC22C2×#14519839
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC22×D8×C61C4
socleC22×C61C2×#102
prime radicalC22×#14519796C2
cosocleC8×D61C24
hypercenterC22×D8#6923
hypocenterC61C2×#2143
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D8

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113613);