Finite Group Databasebeta

C4×#16840712 #30608632

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

Aliases

direct productC4×#16840712

Splittings

FittingC4×C22⋊C4×C61 ⋊ C4
SylowC61 ⋊ C4×#388

Subgroups

subgroupG/H
centerC22×C4C22×#6923
commutatorC22×C61C22×C42
FrattiniC23C23×#6923
FittingC4×C22⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC4×C22⋊C4#6923
hypocenterC61C4×#388
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

2134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1098187);