Finite Group Databasebeta

D4×#14273643 #28604035

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

Aliases

direct productD4×#14273643

Splittings

FittingD4×M16×C59 ⋊ C2
SylowC59 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
FittingD4×M16×C59C2
socleC22×C59C22×C22⋊C4
prime radicalC2×D4×D236C2
cosocleC22×C4×C59C24
hypercenterD4×M16D59
hypocenterC59D4×#100
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

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, 184914);