Finite Group Databasebeta

D59×#1401 #28508894

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD59×#1401

Splittings

FittingC59×#1401 ⋊ C2
SylowC59 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC16D4×D59
commutatorC4×C59C22×C16
FrattiniC2×C16C22×D59
FittingC59×#1401C2
socleC2×C59C2×C22⋊C16
prime radical#41×D59C8
cosocleC2×C16×C59C23
hypercenter#1401D59
hypocenterC59C2×#1401
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C16 ◁ C2×C16 ◁ #1401

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 89773);