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C32×C7×C11⋊C5 #16812374

order3465
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×C11⋊C5
unambiguous semidirect productC11⋊(C32×C5×C7)
unambiguous semidirect product(C3×C11)⋊(C3×C5×C7)
unambiguous semidirect product(C32×C11)⋊(C5×C7)
unambiguous semidirect product(C32×C7×C11)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C32×C5×C7
HallC32×C11 ⋊ C5×C7
HallC7×C11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32×C7C11⋊C5
commutator, cosocle, hypocenterC11C32×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C11C5
LCSG ▷ C11
UCSC1 ◁ C32×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 693

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(7,8,9,10,11,12,13)(15,16,18,21,20)(17,19,23,24,22);(4,5,6)(14,15,17,20,16,18,22,24,19,21,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C7×A4×C11⋊C5, C32×C5×C7×C11⋊C5, C32×C49×C11⋊C5, …
maximal normal subgroup ofC32×C5×C7×C11⋊C5, C32×C49×C11⋊C5, C32×C72×C11⋊C5, …
maximal quotient ofC3×C7×A4×C11⋊C5, C32×C7×C11⋊C25, C32×C5×C7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3465, 7);