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C3×C11×C7⋊(C52⋊C3) #31773159

order17325
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C11×C7⋊(C52⋊C3)
unambiguous semidirect product(C3×C7)⋊(C11×C52⋊C3)
unambiguous semidirect product(C3×C52)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7×C11)⋊(C52⋊C3)
unambiguous semidirect product(C3×C52×C11)⋊ΓL(1,𝔽8)

Splittings

Fitting, socleC3×C52×C7×C11 ⋊ C3
derived, HallC52×C7 ⋊ C32×C11
HallC52×C7×C11 ⋊ C32
HallC52×C11 ⋊ C3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C32×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C3
LCSG ▷ C52×C7
UCSC1 ◁ C3×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

2013 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D7⋊(C52⋊C3), C3×C11⋊(D7⋊(C52⋊C3)), C3×D11×C7⋊(C52⋊C3), …
maximal normal subgroup ofC3×C11×D7⋊(C52⋊C3), C3×C11⋊(D7⋊(C52⋊C3)), C3×D11×C7⋊(C52⋊C3), …
maximal quotient ofC2×C3×C11×C7⋊(C52⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17325, 19);