Finite Group Databasebeta

C2×#21425995 #28742131

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425995

Splittings

SylowC59 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#16837514
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
Fitting, prime radicalC2×C59×#509C2
socleC22×C59#442
cosocleC2×C8×C59C24
hypercenterC2×#509D59
hypocenterC59C2×AGL(1,ℤ/16)
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323010);