Finite Group Databasebeta

D59×#1367 #28500229

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD59×#1367

Splittings

FittingC59×#1367 ⋊ C2
SylowC59 ⋊ C2×#1367

Subgroups

subgroupG/H
centerC2×C8D4×D59
commutatorC4×C59C22×C16
FrattiniC4×C8C22×D59
FittingC59×#1367C2
socleC22×C59C2×C4⋊C8
prime radicalC22×D59C4⋊C8
cosocleC4×C8×C59C23
hypercenter#1367D59
hypocenterC59C2×#1367
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1367

286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 81108);