Finite Group Databasebeta

C2×#21425368 #28616518

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425368

Splittings

FittingC22×#100×C59 ⋊ C2
SylowC59 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#16837318
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#100×C59C2
socleC22×C59#394
prime radicalC22×#14273753C2
hypercenterC22×#100D59
hypocenterC59C2×#2048
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197397);