Finite Group Databasebeta

D4×C16×D59 #28741835

order15104
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productD4×C16×D59

Splittings

FittingD4×C16×C59 ⋊ C2
SylowC59 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC2×C16C22×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingD4×C16×C59C2
socleC22×C59C23×C8
prime radicalC2×D4×D59C8
cosocleC2×C8×C59C24
hypercenterD4×C16D59
hypocenterC59C2×D4×C16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C16 ◁ D4×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322714);