Finite Group Databasebeta

C22×#16839909 #30546334

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16839909

Splittings

FittingC22×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C22×#449

Subgroups

subgroupG/H
centerC24C2×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C2×D4
hypercenterC22×C22⋊C8D61
hypocenterC61C22×#449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

5454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1035889);