Finite Group Databasebeta

C2×#21423450 #28570917

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

Aliases

direct productC2×#21423450

Splittings

FittingC2×C59×#331 ⋊ C2
SylowC59 ⋊ C2×#1667

Subgroups

subgroupG/H
centerC23#14273700
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC2×C59×#331C2
socleC23×C59#121
hypercenterC2×#331D59
hypocenterC59C2×#1667
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 151796);