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C2×#14544631 #17969222

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14544631
unambiguous semidirect productD17⋊#1793

Splittings

FittingC2×C17×2−1+4 ⋊ C4
SylowC17 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC22#11763750
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×2−1+4C4
socleC22×C17#379
prime radicalC2×2−1+4×D17C2
cosocleC2×C4×D17C24
hypercenterC2×2−1+4#595
hypocenterC17C2×#1793
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

3682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104466);