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C4×#11762982 #17040220

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

Aliases

direct productC4×#11762982

Splittings

FittingC4×C17×2−1+4 ⋊ C2
SylowC17 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#10587639
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×2−1+4C2
socleC22×C17C2×#120
prime radicalC2×#11762982C2
cosocleC22×C4×C17C24
hypercenterC4×2−1+4D17
hypocenterC17C4×#454
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×2−1+4

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 175464);