Finite Group Databasebeta

D59×#3372 #29468346

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

Aliases

direct productD59×#3372

Splittings

FittingC59×#3372 ⋊ C2
SylowC59 ⋊ C2×#3372

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC59×#3372C2
socleC22×C59C23×D4
prime radicalC2×D4×D59C23
hypercenter#3372D59
hypocenterC59C2×#3372
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3372

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1049225);