Finite Group Databasebeta

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C2×#14543968 #17963088

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14543968
unambiguous semidirect productD17⋊#1440

Splittings

FittingC22×C22⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1440

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC25×D17C22
cosocleC23×D17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1440
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊C4

4622 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, 1098332);