Finite Group Databasebeta

C22×D61⋊#104 #30625200

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

Aliases

direct productC22×D61⋊#104
unambiguous semidirect productD61⋊(C22×#104)

Splittings

FittingC22×#41×C61 ⋊ C4
SylowC61 ⋊ C23×#104

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
hypocenterC61C23×#104
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

5758 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, 1114755);