Finite Group Databasebeta

C4×#16839641 #29601161

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

Aliases

direct productC4×#16839641

Splittings

FittingC23×C42×C61 ⋊ C2
SylowC61 ⋊ C4×#386

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C22×C42
FrattiniC24C23×D61
FittingC23×C42×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC23×C42D61
hypocenterC61C4×#386
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C23×C42

3366 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, 90716);