Finite Group Databasebeta

C2×#131×Dic59 #29452091

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#131×Dic59

Splittings

SylowC59 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C23×C42
FrattiniC2×C4C24×D59
FittingC22×#131×C59C2
socleC23×C59C23×C4
prime radicalC22×#41×C59C22
cosocleC2×C4×C59C25
hypercenterC22×#131D59
hypocenterC59C2×C4×#131
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C22×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1032970);