Finite Group Databasebeta

D59×#1793 #28587976

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD59×#1793

Splittings

FittingC59×#1793 ⋊ C2
SylowC59 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC22#120×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1793C2
socleC22×C59C2×#120
prime radicalC2×2−1+4×D59C2
cosocleC22×C4×C59C24
hypercenter#1793D59
hypocenterC59C2×#1793
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1793

3682 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, 168855);