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C7×C11×C41⋊C5 #30628905

order15785
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C41⋊C5
unambiguous semidirect productC41⋊(C5×C7×C11)
unambiguous semidirect product(C7×C41)⋊(C5×C11)

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C5
derived, SylowC41 ⋊ C5×C7×C11
HallC11×C41 ⋊ C5×C7
HallC7×C41 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11C41⋊C5
commutator, cosocle, hypocenterC41C5×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C41C5
LCSG ▷ C41
UCSC1 ◁ C7×C11

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

1001 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C11×C41⋊C5, C7×C11×D41⋊C5, C7×D11×C41⋊C5, …
maximal normal subgroup ofC2×C7×C11×C41⋊C5, C7×C11×D41⋊C5, C7×D11×C41⋊C5, …
maximal quotient ofC2×C7×C11×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15785, 2);