Finite Group Databasebeta

C2×#518×D59 #29495266

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#518×D59

Splittings

FittingC2×C59×#518 ⋊ C2
SylowC59 ⋊ C22×#518

Subgroups

subgroupG/H
centerC23C24×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC2×C59×#518C2
socleC23×C59C25
prime radicalC23×D4×D59C2
cosocleC22×C59C26
hypercenterC2×#518D59
hypocenterC59C22×#518
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#518

14590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076145);