Finite Group Databasebeta

C2×#21422343 #28510355

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21422343

Splittings

SylowC59 ⋊ C2×#1440

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC23×C22⋊C4×C59C2
socleC25×C59C23
prime radicalC26×C59C22
cosocleC24×C59C24
hypercenterC23×C22⋊C4D59
hypocenterC59C2×#1440
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C22⋊C4

4622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 91234);