Finite Group Databasebeta

C2×#21462055 #30623878

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21462055

Splittings

SylowC61 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC22×C61C23×C8
FrattiniC2×C4C23×#6923
Fitting, prime radicalC22×#41×C61C4
socleC22×C61C2×C22⋊C8
cosocleC2×#92418C24
hypercenterC22×#41#6923
hypocenterC61C2×#2115
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113433);