Finite Group Databasebeta

D59×#1276 #28478123

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productD59×#1276

Splittings

FittingC59×#1276 ⋊ C2
SylowC59 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC42D4×D59
commutatorC4×C59C2×C4×C8
FrattiniC2×C42C22×D59
FittingC59×#1276C2
socleC22×C59C2×#95
prime radicalC23×D59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1276D59
hypocenterC59C2×#1276
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1276

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 59002);