Finite Group Databasebeta

C22×#16840709 #30624569

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#16840709
unambiguous semidirect productD61⋊(C2×#385)

Splittings

FittingC22×C22⋊C4×C61 ⋊ C4
SylowC61 ⋊ C22×#385

Subgroups

subgroupG/H
centerC24C22×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC22×C22⋊C4×C61C4
socleC24×C61C22×C4
prime radicalC25×D61C22
cosocleC22×D61C25
hypercenterC22×C22⋊C4#6923
hypocenterC61C22×#385
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114124);