Finite Group Databasebeta

D59×#2115 #28741376

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD59×#2115

Splittings

FittingC59×#2115 ⋊ C2
SylowC59 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC8C22⋊C4×D59
commutatorC22×C59C23×C8
FrattiniC2×C8C23×D59
FittingC59×#2115C2
socleC2×C59C22×C22⋊C8
prime radicalC2×#41×D59C4
cosocleC2×C8×C59C24
hypercenter#2115D59
hypocenterC59C2×#2115
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2115

1154 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, 322255);