Finite Group Databasebeta

D4×C22⋊C4×D59 #28747856

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productD4×C22⋊C4×D59

Splittings

FittingD4×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingD4×C22⋊C4×C59C2
socle, cosocleC23×C59C25
prime radicalC23×D4×D59C2
hypercenterD4×C22⋊C4D59
hypocenterC59C2×D4×C22⋊C4
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ D4×C22⋊C4

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 328735);