Finite Group Databasebeta

D59×#2153 #28741686

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD59×#2153

Splittings

FittingC59×#2153 ⋊ C2
SylowC59 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC8C2×D4×D59
commutatorC4×C59C23×C8
FrattiniC2×C8C23×D59
FittingC59×#2153C2
socleC2×C59C22×C4⋊C8
prime radicalC23×D59M16
cosocleC2×C8×C59C24
hypercenter#2153D59
hypocenterC59C2×#2153
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2153

698 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, 322565);