Finite Group Databasebeta

D59×#1378 #28503552

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

Aliases

direct productD59×#1378

Splittings

FittingC59×#1378 ⋊ C2
SylowC59 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC8C22⋊C4×D59
commutatorC22×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC59×#1378C2
socleC2×C59C2×#336
prime radicalC23×D59C2×C8
cosocleC22×C8×C59C23
hypercenter#1378D59
hypocenterC59C2×#1378
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1378

586 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, 84431);