Finite Group Databasebeta

C2×#21426076 #28742638

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

Aliases

direct productC2×#21426076

Splittings

FittingC2×C59×#350 ⋊ C2
SylowC59 ⋊ C2×#2195

Subgroups

subgroupG/H
centerC22#16837538
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC2×C59×#350C2
socleC22×C59#447
prime radicalC2×#16838219C2
hypercenterC2×#350D59
hypocenterC59C2×#2195
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 323517);