Finite Group Databasebeta

C2×#21427691 #28756704

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

Aliases

direct productC2×#21427691

Splittings

SylowC59 ⋊ C2×#2429

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×C22⋊Q8×C59C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC22×C22⋊Q8D59
hypocenterC59C2×#2429
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 337583);