Finite Group Databasebeta

C2×D61⋊#443 #30625471

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D61⋊#443
unambiguous semidirect productD61⋊(C2×#443)

Splittings

FittingC2×#135×C61 ⋊ C4
SylowC61 ⋊ C22×#443

Subgroups

subgroupG/H
centerC2×C4D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC2×#135×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#135×D61C2
cosocleC4×D61C25
hypercenterC2×#135#6923
hypocenterC61C22×#443
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1115026);