Finite Group Databasebeta

C2×#21425402 #28616606

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

Aliases

direct productC2×#21425402

Splittings

FittingC2×C59×#424 ⋊ C2
SylowC59 ⋊ C2×#2053

Subgroups

subgroupG/H
centerC2×C4#14273716
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#424C2
socleC22×C59#394
prime radicalC2×#16838202C2
hypercenterC2×#424D59
hypocenterC59C2×#2053
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#424

1366 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, 197485);