Finite Group Databasebeta

C2×#21425148 #28615681

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21425148

Splittings

FittingC2×C59×#410 ⋊ C2
SylowC59 ⋊ C2×#2008

Subgroups

subgroupG/H
centerC22#16837311
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#410C2
socleC22×C59#392
hypercenterC2×#410D59
hypocenterC59C2×#2008
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

2118 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, 196560);