Finite Group Databasebeta

C4×#11762991 #17040229

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#11762991

Splittings

FittingC4×C17×C4⋊Q8 ⋊ C2
SylowC17 ⋊ C4×#456

Subgroups

subgroupG/H
centerC2×C4#10587623
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×C4⋊Q8C2
socleC22×C17C2×#120
prime radicalC2×#10587694C22
cosocleC22×C4×C17C24
hypercenterC4×C4⋊Q8D17
hypocenterC17C4×#456
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊Q8

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 175473);