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C4×C7×C11⋊C5 #13095349

order1540
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C7)
unambiguous semidirect product(C4×C7×C11)⋊C5

Splittings

Fitting, HallC4×C7×C11 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5
HallC4×C11 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC4×C7C11⋊C5
commutator, hypocenterC11C4×C5×C7
FrattiniC2C2×C7×C11⋊C5
FittingC4×C7×C11C5
socleC2×C7×C11C2×C5
prime radicalC2×C7×C11⋊C5C2
cosocleC2×C11C2×C5×C7
LCSG ▷ C11
UCSC1 ◁ C4×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 308

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C7×C11⋊C5, C4×ΓL(1,𝔽8)×C11⋊C5, C7×Dic3×C11⋊C5, …
maximal normal subgroup ofC3×C4×C7×C11⋊C5, C4×ΓL(1,𝔽8)×C11⋊C5, C4×C7×C11×C11⋊C5, …
maximal quotient ofC3×C4×C7×C11⋊C5, C7×Dic3×C11⋊C5, C7×#157×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1540, 4);