Finite Group Databasebeta

D59×#1376 #28503540

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1376

Splittings

FittingC59×#1376 ⋊ C2
SylowC59 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC2×C8D4×D59
commutatorC4×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC59×#1376C2
socleC22×C59C2×C4⋊C8
prime radicalC23×D59M16
cosocleC22×C8×C59C23
hypercenter#1376D59
hypocenterC59C2×#1376
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1376

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84419);