Finite Group Databasebeta

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C3×C7×A4×C17 #16862830

order4284
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C7×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C7×A4×C17
unambiguous semidirect productC22⋊(C32×C7×C17)
unambiguous semidirect product(C22×C3)⋊(C3×C7×C17)
unambiguous semidirect product(C22×C17)⋊(C32×C7)
unambiguous semidirect product(C22×C3×C17)⋊(C3×C7)

Splittings

Fitting, socleC22×C3×C7×C17 ⋊ C3
derived, SylowC22 ⋊ C32×C7×C17
HallC22×C7×C17 ⋊ C32
HallC22×C17 ⋊ C32×C7
HallC22×C7 ⋊ C32×C17

Subgroups

subgroupG/H
center, hypercenterC3×C7×C17A4
commutator, cosocle, hypocenterC22C32×C7×C17
FrattiniC1G
Fitting, socleC22×C3×C7×C17C3
LCSG ▷ C22
UCSC1 ◁ C3×C7×C17

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1428

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C7×A4×C17, C3×C7×C17×A5, C3×A4×C17×C49, …
maximal normal subgroup ofC3×C5×C7×A4×C17, C3×A4×C17×C49, C3×C72×A4×C17
maximal quotient ofC3×C5×C7×A4×C17, C3×A4×C17×C49, C7×A4×C17×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4284, 117);