Finite Group Databasebeta

C2×#21422238 #28508896

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21422238

Splittings

SylowC59 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C16C22⋊D59
commutatorC4×C59C22×C16
FrattiniC2×C16C22×D59
FittingC2×C59×#504C2
socleC22×C59C22⋊C16
prime radicalC2×#41×C59C8
cosocleC2×C16×C59C23
hypercenterC2×#504D59
hypocenterC59C2×#1401
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C2×#504

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 89775);