Finite Group Databasebeta

C4×#16839743 #29677687

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#16839743

Splittings

FittingC4×#100×C61 ⋊ C2
SylowC61 ⋊ C4×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC22×C61C22×C42
FrattiniC22×C4C23×D61
FittingC4×#100×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C22
cosocleC22×C4×C61C24
hypercenterC4×#100D61
hypocenterC61C4×#413
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 167242);