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C17×C22⋊(C52⋊C3) #19099834

order5100
isoclinismisoclinic class of C22⋊(C52⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C17 · Schur multiplier (H2) = C2×C5

Aliases

direct productC17×C22⋊(C52⋊C3)
unambiguous semidirect productC22⋊(C17×C52⋊C3)
unambiguous semidirect productC52⋊(A4×C17)
unambiguous semidirect product(C22×C17)⋊(C52⋊C3)
unambiguous semidirect product(C52×C17)⋊A4

Splittings

Fitting, socle, HallC22×C52×C17 ⋊ C3
derived, HallC22×C52 ⋊ C3×C17
HallC52×C17 ⋊ A4
HallC22×C17 ⋊ C52⋊C3
SylowC52 ⋊ A4×C17
SylowC22 ⋊ C17×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C22⋊(C52⋊C3)
commutator, hypocenterC22×C52C3×C17
FrattiniC1G
Fitting, socleC22×C52×C17C3
LCSG ▷ C22×C52
UCSC1 ◁ C17

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

612 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C17×C52⋊C3, C3×C17×C22⋊(C52⋊C3), C7×C17×C22⋊(C52⋊C3), …
maximal normal subgroup ofA4×C17×C52⋊C3, C3×C17×C22⋊(C52⋊C3), C7×C17×C22⋊(C52⋊C3)
maximal quotient ofC17×C22⋊(C52⋊C9), C3×C17×C22⋊(C52⋊C3), C7×C17×C22⋊(C52⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 137);