Finite Group Databasebeta

C2×#21433447 #29455319

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21433447

Splittings

FittingC22×#104×C59 ⋊ C2
SylowC59 ⋊ C2×#3018

Subgroups

subgroupG/H
centerC2×C4#14273697
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#104×C59C2
socleC22×C59C2×#120
hypercenterC22×#104D59
hypocenterC59C2×#3018
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

4850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036198);