Finite Group Databasebeta

C2×#21422421 #28554524

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

Aliases

direct productC2×#21422421

Splittings

FittingC2×C59×#323 ⋊ C2
SylowC59 ⋊ C2×#1462

Subgroups

subgroupG/H
centerC23C22⋊C4×D59
commutatorC23×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#323C2
socleC23×C59C2×C22⋊C4
prime radicalC25×D59C4
cosocleC22×C4×C59C24
hypercenterC2×#323D59
hypocenterC59C2×#1462
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 135403);