Finite Group Databasebeta

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C4×#11763077 #17041200

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11763077

Splittings

FittingC4×C17×AGL(1,ℤ/8) ⋊ C2
SylowC17 ⋊ C4×#472

Subgroups

subgroupG/H
centerC2×C4#10587625
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×AGL(1,ℤ/8)C2
socleC22×C17C2×#121
prime radicalC2×#11763077C2
cosocleC22×C4×C17C24
hypercenterC4×AGL(1,ℤ/8)D17
hypocenterC17C4×#472
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 176444);