Finite Group Databasebeta

C2×#21424281 #28589346

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21424281

Splittings

SylowC59 ⋊ C2×#1851

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×C22⋊C4×C59C2
socleC24×C59C22×C4
prime radicalC25×C59C2×C4
cosocleC22×C4×C59C24
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C2×#1851
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

1702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 170225);