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C2×#14544471 #17968191

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14544471

Splittings

FittingC22×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1736

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1736
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103435);