Finite Group Databasebeta

C22×#16840752 #30625188

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16840752
unambiguous semidirect productD61⋊(C2×#416)

Splittings

FittingC22×#41×C61 ⋊ C4
SylowC61 ⋊ C22×#416

Subgroups

subgroupG/H
centerC22×C4C22⋊#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC22×#41×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#41×D61C2
cosocleC4×D61C25
hypercenterC22×#41#6923
hypocenterC61C22×#416
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 1114743);