Finite Group Databasebeta

#104×C22⋊D61 #29695683

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#104×C22⋊D61

Splittings

FittingC22×#104×C61 ⋊ C2
SylowC61 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#104×C61C2
socleC22×C61C22×C22⋊C4
prime radical#41×C22⋊D61C2
cosocleC22×C4×C61C24
hypercenterC22×#104D61
hypocenterC61D4×#104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 185238);