Finite Group Databasebeta

D59×#1336 #28498478

order15104
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD59×#1336

Splittings

FittingC59×#1336 ⋊ C2
SylowC59 ⋊ C2×#1336

Subgroups

subgroupG/H
centerC4#102×D59
commutatorC8×C59C22×C8
FrattiniC4×C8C22×D59
FittingC59×#1336C2
socleC2×C59C2×D4⋊C8
prime radical#135×D59C4
cosocleC4×C8×C59C23
hypercenter#1336D59
hypocenterC59C2×#1336
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #1336

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 79357);