Finite Group Databasebeta

D4×C4⋊#92418 #29698035

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD4×C4⋊#92418

Splittings

SylowC61 ⋊ D4×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D61
commutatorC22×C61C23×C8
FittingC42×D4×C61C2
socleC23×C61C23×C4
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC42×D4D61
hypocenterC61D4×C4⋊C8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C42×D4

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 187590);