Finite Group Databasebeta

D4×#14273653 #28604357

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14273653

Splittings

FittingD4×M16×C59 ⋊ C2
SylowC59 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×M16×C59C2
socleC22×C59C22×C22⋊C4
prime radicalD4×#11745685C2
cosocleC22×C4×C59C24
hypercenterD4×M16D59
hypocenterC59D4×#104
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 185236);