Finite Group Databasebeta

C2×#21421969 #28478602

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21421969

Splittings

SylowC59 ⋊ C2×#1291

Subgroups

subgroupG/H
centerC23C59⋊#95
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC2×C59×#432C2
socleC23×C59#95
prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#432D59
hypocenterC59C2×#1291
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59481);