Finite Group Databasebeta

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C2×#120×#595 #17978894

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#120×#595
unambiguous semidirect productD17⋊(C4×#120)

Splittings

FittingC2×C17×#120 ⋊ C4
SylowC17 ⋊ C2×C4×#120

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#120C4
socleC23×C17C23×C4
prime radicalC2×#120×D17C2
cosocleC22×D17C25
hypercenterC2×#120#595
hypocenterC17C2×C4×#120
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#120

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

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, 1114138);