Finite Group Databasebeta

C2×#21433497 #29455422

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#21433497

Splittings

FittingC2×C59×#535 ⋊ C2
SylowC59 ⋊ C2×#3027

Subgroups

subgroupG/H
centerC22C2×#14273695
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#535C2
socleC22×C59C2×#120
hypercenterC2×#535D59
hypocenterC59C2×#3027
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#535

5110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036301);