Finite Group Databasebeta

D59×#3246 #29461465

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD59×#3246

Splittings

FittingC59×#3246 ⋊ C2
SylowC59 ⋊ C2×#3246

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3246C2
socleC22×C59C23×D4
prime radical#532×D59C2
hypercenter#3246D59
hypocenterC59C2×#3246
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

2178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1042344);