Finite Group Databasebeta

C22⋊C4×#11758198 #29601413

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×#11758198

Splittings

FittingC2×C4×C22⋊C4×C61 ⋊ C2
SylowC61 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C22⋊C42
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 90968);