Finite Group Databasebeta

C2×#21444057 #29601149

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21444057

Splittings

FittingC23×C42×C61 ⋊ C2
SylowC61 ⋊ C2×#1437

Subgroups

subgroupG/H
centerC25C22×D61
commutatorC22×C61C22×C42
FrattiniC24C23×D61
FittingC23×C42×C61C2
socleC25×C61C23
prime radicalC25×D61C22
cosocleC24×C61C24
hypercenterC23×C42D61
hypocenterC61C2×#1437
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C25 ◁ C23×C42

5230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 90704);