Finite Group Databasebeta

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C2×2−1+4×#595 #17981041

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×#595
unambiguous semidirect productD17⋊(C4×2−1+4)

Splittings

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

Subgroups

subgroupG/H
centerC22C24×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC2×C17×2−1+4C4
socleC22×C17C24×C4
prime radicalC2×2−1+4×D17C2
cosocleC2×D17C26
hypercenterC2×2−1+4#595
hypocenterC17C2×C4×2−1+4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116285);