Finite Group Databasebeta

D59×#1841 #28588950

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1841

Splittings

FittingC59×#1841 ⋊ C2
SylowC59 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC4#117×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1841C2
socleC2×C59C2×#383
prime radicalC23×D59#41
cosocleC22×C4×C59C24
hypercenter#1841D59
hypocenterC59C2×#1841
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1841

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 169829);