Finite Group Databasebeta

D59×#2225 #28743308

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

Aliases

direct productD59×#2225

Splittings

FittingC59×#2225 ⋊ C2
SylowC59 ⋊ C2×#2225

Subgroups

subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2225C2
socleC22×C59C22×D8
prime radicalC22×D59C2×D8
hypercenter#2225D59
hypocenterC59C2×#2225
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324187);