Finite Group Databasebeta

C22×#16837663 #29456060

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16837663

Splittings

SylowC59 ⋊ C22×#471

Subgroups

subgroupG/H
centerC23#14273699
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC22×AGL(1,ℤ/8)×C59C2
socleC23×C59#121
hypercenterC22×AGL(1,ℤ/8)D59
hypocenterC59C22×#471
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036939);