Finite Group Databasebeta

C4×#16840741 #30614056

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

Aliases

direct productC4×#16840741

Splittings

FittingC22×C42×C61 ⋊ C4
SylowC61 ⋊ C4×#410

Subgroups

subgroupG/H
centerC42C22⋊#6923
commutatorC22×C61C22×C42
FrattiniC23C23×#6923
FittingC22×C42×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C22
cosocleC23×D61C24
hypercenterC22×C42#6923
hypocenterC61C4×#410
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ C22×C42

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103611);