Finite Group Databasebeta

C2×#21433816 #29456084

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

Aliases

direct productC2×#21433816

Splittings

FittingC22×#131×C59 ⋊ C2
SylowC59 ⋊ C2×#3067

Subgroups

subgroupG/H
centerC2×C4#14273701
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#131×C59C2
socleC22×C59C2×#121
hypercenterC22×#131D59
hypocenterC59C2×#3067
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#131

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036963);