Finite Group Databasebeta

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C4×#11762576 #16939527

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11762576

Splittings

SylowC17 ⋊ C4×#342

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC22×C17C43
FrattiniC25C22×D17
FittingC2×C4×C22⋊C4×C17C2
socleC23×C17C2×C22⋊C4
prime radical, cosocleC25×C17C23
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C4×#342
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 74771);