Finite Group Databasebeta

D59×#2183 #28742172

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productD59×#2183

Splittings

FittingC59×#2183 ⋊ C2
SylowC59 ⋊ C2×#2183

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D59
commutator, socleC22×C59C23×C8
FittingC59×#2183C2
prime radicalC22×D59C22×C8
cosocleC2×C8×C59C24
hypercenter#2183D59
hypocenterC59C2×#2183
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ #2183

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 323051);