Finite Group Databasebeta

D59×#1828 #28588541

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD59×#1828

Splittings

FittingC59×#1828 ⋊ C2
SylowC59 ⋊ C2×#1828

Subgroups

subgroupG/H
centerC2#381×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC59×#1828C2
socleC2×C59C2×#381
prime radicalC22×D4×D59C22
cosocleC24×C59C24
hypercenter#1828D59
hypocenterC59C2×#1828
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C24 ◁ #1828

1554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 169420);