Finite Group Databasebeta

C4×#16839768 #29677791

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#16839768

Splittings

FittingC2×C4×M16×C61 ⋊ C2
SylowC61 ⋊ C4×#418

Subgroups

subgroupG/H
centerC22×C4C2×D244
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C4×M16×C61C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenterC2×C4×M16D61
hypocenterC61C4×#418
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

2018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167346);