Finite Group Databasebeta

C4×#131×D59 #29452089

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

Aliases

direct productC4×#131×D59

Splittings

FittingC4×#131×C59 ⋊ C2
SylowC59 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC4×C8C22×D59
commutatorC2×C59C23×C42
FrattiniC2×C4C24×D59
FittingC4×#131×C59C2
socleC22×C59C24×C4
prime radicalC2×#41×D59C22
cosocleC2×C4×C59C25
hypercenterC4×#131D59
hypocenterC59C2×C4×#131
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C8 ◁ C4×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1032968);