Finite Group Databasebeta

C2×#21433475 #29455351

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

Aliases

direct productC2×#21433475

Splittings

SylowC59 ⋊ C2×#3022

Subgroups

subgroupG/H
centerC22C2×#14273696
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#585C2
socleC22×C59C2×#120
hypercenterC2×#585D59
hypocenterC59C2×#3022
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#585

4742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1036230);