Finite Group Databasebeta

D59×#1384 #28503596

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productD59×#1384

Splittings

FittingC59×#1384 ⋊ C2
SylowC59 ⋊ C2×#1384

Subgroups

subgroupG/H
centerC4#106×D59
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC59×#1384C2
socleC2×C59C2×#340
prime radicalC23×D59D8
cosocleC22×C8×C59C23
hypercenter#1384D59
hypocenterC59C2×#1384
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1384

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84475);