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C2×#14544623 #17969194

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

Aliases

direct productC2×#14544623
unambiguous semidirect productD17⋊#1787

Splittings

FittingC23×Q8×C17 ⋊ C4
SylowC17 ⋊ C2×#1787

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC23×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC23×Q8#595
hypocenterC17C2×#1787
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

3942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104438);