Finite Group Databasebeta

D59×#1296 #28478771

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1296

Splittings

FittingC59×#1296 ⋊ C2
SylowC59 ⋊ C2×#1296

Subgroups

subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1296D59
hypocenterC59C2×#1296
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59650);