Finite Group Databasebeta

C2×#556×D59 #29495697

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

Aliases

direct productC2×#556×D59

Splittings

FittingC2×C59×#556 ⋊ C2
SylowC59 ⋊ C22×#556

Subgroups

subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#556C2
socleC23×C59C25
prime radicalC22×D4×D59C22
hypercenterC2×#556D59
hypocenterC59C22×#556
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#556

7846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076576);