Finite Group Databasebeta

D59×#2110 #28741344

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productD59×#2110

Splittings

FittingC59×#2110 ⋊ C2
SylowC59 ⋊ C2×#2110

Subgroups

subgroupG/H
centerC8C42×D59
commutatorC4×C59C22×C42
FrattiniC2×C8C23×D59
FittingC59×#2110C2
socleC2×C59C22×#97
prime radicalC23×D59M16
cosocleC2×C8×C59C24
hypercenter#2110D59
hypocenterC59C2×#2110
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C8 ◁ #2110

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322223);