Finite Group Databasebeta

C2×#21433824 #29456093

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

Aliases

direct productC2×#21433824

Splittings

FittingC2×C59×#568 ⋊ C2
SylowC59 ⋊ C2×#3068

Subgroups

subgroupG/H
centerC22C2×#14273701
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#568C2
socleC22×C59C2×#121
hypercenterC2×#568D59
hypocenterC59C2×#3068
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

2746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036972);