Finite Group Databasebeta

C22×C4×C4⋊#6923 #30624539

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×C4⋊#6923

Splittings

FittingC22×C42×C61 ⋊ C4
SylowC61 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×#6923
commutatorC2×C61C23×C42
FrattiniC22C24×#6923
FittingC22×C42×C61C4
socleC24×C61C22×C4
prime radicalC24×D61C23
cosocleC22×D61C25
hypercenterC22×C42#6923
hypocenterC61C22×C4×C4⋊C4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C42

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114094);