Finite Group Databasebeta

C2×#21426268 #28743420

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

Aliases

direct productC2×#21426268

Splittings

FittingC2×C59×#364 ⋊ C2
SylowC59 ⋊ C2×#2230

Subgroups

subgroupG/H
centerC22#16837693
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#364C2
socleC22×C59#476
prime radicalC2×#14273749C22
hypercenterC2×#364D59
hypocenterC59C2×#2230
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1670 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 324299);