Finite Group Databasebeta

C22×C22⋊Q8×D61 #30586652

order15616
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×C22⋊Q8×D61

Splittings

FittingC22×C22⋊Q8×C61 ⋊ C2
SylowC61 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC24C23×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC22×C22⋊Q8×C61C2
socleC24×C61C24
prime radicalC25×D61C22
hypercenterC22×C22⋊Q8D61
hypocenterC61C23×C22⋊Q8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076207);