Finite Group Databasebeta

C2×#22561498 #30883695

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

Aliases

direct productC2×#22561498

Splittings

SylowC67 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#14524015
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
Fitting, prime radicalC22×AGL(1,ℤ/8)×C67C2
socleC23×C67#121
hypercenterC22×AGL(1,ℤ/8)D67
hypocenterC67C2×#2051
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197432);