Finite Group Databasebeta

D59×#2170 #28741913

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD59×#2170

Splittings

FittingC59×#2170 ⋊ C2
SylowC59 ⋊ C2×#2170

Subgroups

subgroupG/H
centerC16D4×D59
commutatorC4×C59C23×C8
FrattiniC2×C8C23×D59
FittingC59×#2170C2
socleC2×C59C2×C8×D4
prime radical#135×D59C4
cosocleC2×C8×C59C24
hypercenter#2170D59
hypocenterC59C2×#2170
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C16 ◁ C2×C16 ◁ #2170

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 322792);