Finite Group Databasebeta

C22×#16840632 #30613864

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

Aliases

direct productC22×#16840632

Splittings

FittingC22×C4⋊C4×C61 ⋊ C4
SylowC61 ⋊ C22×#339

Subgroups

subgroupG/H
centerC24C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC22×C4⋊C4×C61C4
socleC24×C61C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C22×#339
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

2830 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, 1103419);