Finite Group Databasebeta

D4×C4⋊C4×D61 #29839293

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×C4⋊C4×D61

Splittings

FittingD4×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingD4×C4⋊C4×C61C2
socle, cosocleC23×C61C25
prime radicalC22×D4×D61C22
hypercenterD4×C4⋊C4D61
hypocenterC61C2×D4×C4⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ D4×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 328848);