Finite Group Databasebeta

C2×#21422456 #28554655

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

Aliases

direct productC2×#21422456

Splittings

SylowC59 ⋊ C2×#1471

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC22×#121×C59C2
socleC23×C59C2×C22⋊C4
cosocleC22×C4×C59C24
hypercenterC22×#121D59
hypocenterC59C2×#1471
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

1770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 135534);