Finite Group Databasebeta

D59×#3166 #29458340

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

Aliases

direct productD59×#3166

Splittings

FittingC59×#3166 ⋊ C2
SylowC59 ⋊ C2×#3166

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3166C2
socleC22×C59C23×D4
prime radicalC23×D59C2×D4
hypercenter#3166D59
hypocenterC59C2×#3166
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1039219);