Finite Group Databasebeta

D59×#2296 #28747066

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD59×#2296

Splittings

FittingC59×#2296 ⋊ C2
SylowC59 ⋊ C2×#2296

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC59×#2296C2
socle, cosocleC23×C59C25
prime radicalC24×D59C23
hypercenter#2296D59
hypocenterC59C2×#2296
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2296

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 327945);