Finite Group Databasebeta

C2×#21428306 #28757188

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21428306

Splittings

SylowC59 ⋊ C2×#2478

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×#117×C59C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC22×#117D59
hypocenterC59C2×#2478
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#117

2638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 338067);