Finite Group Databasebeta

C2×#21423046 #28560757

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

Aliases

direct productC2×#21423046

Splittings

FittingC2×C59×#448 ⋊ C2
SylowC59 ⋊ C2×#1601

Subgroups

subgroupG/H
centerC23#14273695
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#448C2
socleC23×C59#120
prime radicalC2×#16837960C2
hypercenterC2×#448D59
hypocenterC59C2×#1601
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

1652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 141636);