Finite Group Databasebeta

C22×#16840801 #30625444

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

Aliases

direct productC22×#16840801
unambiguous semidirect productD61⋊(C2×#440)

Splittings

FittingC22×SD16×C61 ⋊ C4
SylowC61 ⋊ C22×#440

Subgroups

subgroupG/H
centerC23D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC22×SD16×C61C4
socleC23×C61C4×D4
prime radicalC22×D4×D61C22
cosocleC4×D61C25
hypercenterC22×SD16#6923
hypocenterC61C22×#440
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

3222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114999);