Finite Group Databasebeta

C2×#21447108 #29707877

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447108

Splittings

SylowC61 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC22×AGL(1,ℤ/8)×C61C2
socleC23×C61#121
hypercenterC22×AGL(1,ℤ/8)D61
hypocenterC61C2×#2051
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 197432);