Finite Group Databasebeta

C2×#21438598 #29496138

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

Aliases

direct productC2×#21438598

Splittings

FittingC2×C59×#529 ⋊ C2
SylowC59 ⋊ C2×#3557

Subgroups

subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
prime radicalC2×#16838005C2
hypercenterC2×#529D59
hypocenterC59C2×#3557
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#529

6554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1077017);