Finite Group Databasebeta

D4×#14273644 #28604040

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

Aliases

direct productD4×#14273644

Splittings

SylowC59 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic59
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×D42×C59C2
socleC22×C59C22×C22⋊C4
cosocleC22×C4×C59C24
hypercenterC2×D42D59
hypocenterC59D4×#100
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D42

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 184919);