Finite Group Databasebeta

C2×#21423404 #28569811

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#21423404

Splittings

FittingC2×C59×#329 ⋊ C2
SylowC59 ⋊ C2×#1659

Subgroups

subgroupG/H
centerC23#14273697
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#329C2
socleC23×C59#120
prime radicalC2×#16838144C2
hypercenterC2×#329D59
hypocenterC59C2×#1659
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 150690);