Finite Group Databasebeta

D59×#1583 #28558189

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1583

Splittings

FittingC59×#1583 ⋊ C2
SylowC59 ⋊ C2×#1583

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1583C2
socleC22×C59C2×C4×D4
prime radicalC2×D4×D59C2×C4
cosocleC42×C59C24
hypercenter#1583D59
hypocenterC59C2×#1583
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 139068);