Finite Group Databasebeta

D59×#1374 #28503524

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1374

Splittings

FittingC59×#1374 ⋊ C2
SylowC59 ⋊ C2×#1374

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D59
commutatorC2×C59C2×C4×C16
FittingC59×#1374C2
socleC23×C59C22×C8
prime radicalC23×D59C2×C8
cosocleC22×C8×C59C23
hypercenter#1374D59
hypocenterC59C2×#1374
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ #1374

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84403);