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C2×D17⋊#332 #17966017

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

Aliases

direct productC2×D17⋊#332
unambiguous semidirect productD17⋊(C2×#332)

Splittings

SylowC17 ⋊ C22×#332

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×C4⋊Q8C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC4×Dic17C24
hypercenterC2×C4⋊Q8#595
hypocenterC17C22×#332
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

1334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101261);