Finite Group Databasebeta

C2×#21437785 #29496602

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#21437785

Splittings

FittingC23×C22⋊C4×C59 ⋊ C2
SylowC59 ⋊ C2×#3490

Subgroups

subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC23×C22⋊C4×C59C2
socleC23×C59C25
hypercenterC23×C22⋊C4D59
hypocenterC59C2×#3490
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C22⋊C4

9502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 1077481);