Finite Group Databasebeta

C2×D61⋊#353 #30623947

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

Aliases

direct productC2×D61⋊#353
unambiguous semidirect productD61⋊(C2×#353)

Splittings

FittingC2×#127×C61 ⋊ C4
SylowC61 ⋊ C22×#353

Subgroups

subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#127×C61C4
socleC22×C61C2×#99
prime radicalC2×#127×D61C2
cosocleC2×D244C24
hypercenterC2×#127#6923
hypocenterC61C22×#353
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#127

2062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1113502);