Finite Group Databasebeta

D59×#2012 #28615727

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD59×#2012

Splittings

FittingC59×#2012 ⋊ C2
SylowC59 ⋊ C2×#2012

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2012C2
socleC23×C59C22×D4
prime radicalC22×D8×D59C2
hypercenter#2012D59
hypocenterC59C2×#2012
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

2382 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, 196606);