Finite Group Databasebeta

C2×#21425652 #28618574

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21425652

Splittings

FittingC2×C59×#424 ⋊ C2
SylowC59 ⋊ C2×#2098

Subgroups

subgroupG/H
centerC2×C4#14273723
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#424C2
socleC22×C59#399
prime radicalC22×#11745685C22
hypercenterC2×#424D59
hypocenterC59C2×#2098
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

1010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 199453);