Finite Group Databasebeta

D59×#3360 #29468255

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD59×#3360

Splittings

FittingC59×#3360 ⋊ C2
SylowC59 ⋊ C2×#3360

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3360C2
socleC22×C59C23×D4
prime radicalC2×D8×D59C22
hypercenter#3360D59
hypocenterC59C2×#3360
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3360

1906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1049134);