Finite Group Databasebeta

D59×#2231 #28743421

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD59×#2231

Splittings

FittingC59×#2231 ⋊ C2
SylowC59 ⋊ C2×#2231

Subgroups

subgroupG/H
centerC2#476×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2231C2
socleC2×C59C2×#476
prime radical#135×D59C22
hypercenter#2231D59
hypocenterC59C2×#2231
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2231

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324300);