Finite Group Databasebeta

C2×#21433834 #29456104

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

Aliases

direct productC2×#21433834

Splittings

FittingC2×C59×#430 ⋊ C2
SylowC59 ⋊ C2×#3069

Subgroups

subgroupG/H
centerC22C2×#14273702
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#430C2
socleC22×C59C2×#121
prime radicalC2×#16838202C2
hypercenterC2×#430D59
hypocenterC59C2×#3069
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#430

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1036983);