Finite Group Databasebeta

C2×#21429085 #28760479

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

Aliases

direct productC2×#21429085

Splittings

SylowC59 ⋊ C2×#2546

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×C4⋊Q8×C59C2
socle, prime radicalC24×C59C24
hypercenterC22×C4⋊Q8D59
hypocenterC59C2×#2546
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

3094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 341358);