Finite Group Databasebeta

C2×#21437896 #29496591

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

Aliases

direct productC2×#21437896

Splittings

FittingC2×C59×#543 ⋊ C2
SylowC59 ⋊ C2×#3501

Subgroups

subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#543C2
socleC23×C59C25
prime radicalC23×C22⋊D59C22
hypercenterC2×#543D59
hypocenterC59C2×#3501
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#543

7738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1077470);