Finite Group Databasebeta

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C2×#14544808 #17970025

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

Aliases

direct productC2×#14544808

Splittings

FittingC22×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D68C22
cosocleC23×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1899
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105269);