Finite Group Databasebeta

C2×#21427072 #28748175

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21427072

Splittings

FittingC2×C59×#385 ⋊ C2
SylowC59 ⋊ C2×#2358

Subgroups

subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#385C2
socleC24×C59C24
prime radicalC22×#14273697C2
cosocleC23×C59C25
hypercenterC2×#385D59
hypocenterC59C2×#2358
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

5942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 329054);