Finite Group Databasebeta

D59×#1294 #28478671

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

Aliases

direct productD59×#1294

Splittings

FittingC59×#1294 ⋊ C2
SylowC59 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C2×C42
FrattiniC23×C4C22×D59
FittingC59×#1294C2
socleC23×C59C2×C22⋊C4
prime radicalC24×D59D4
cosocleC23×C4×C59C23
hypercenter#1294D59
hypocenterC59C2×#1294
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 59550);