Finite Group Databasebeta

D59×#1812 #28588327

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

Aliases

direct productD59×#1812

Splittings

FittingC59×#1812 ⋊ C2
SylowC59 ⋊ C2×#1812

Subgroups

subgroupG/H
centerC4#117×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1812C2
socleC2×C59C2×#380
prime radicalC2×#41×D59C22
cosocleC22×C4×C59C24
hypercenter#1812D59
hypocenterC59C2×#1812
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1812

1346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 169206);