Finite Group Databasebeta

C2×#22561479 #30883658

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561479

Splittings

SylowC67 ⋊ C2×#2048

Subgroups

subgroupG/H
centerC22#16863310
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
Fitting, prime radicalC22×AGL(1,ℤ/8)×C67C2
socleC22×C67#394
hypercenterC22×AGL(1,ℤ/8)D67
hypocenterC67C2×#2048
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197395);