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C5×C11⋊#157 #14520455

order1980
isoclinismisoclinic class of C11⋊#157
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11⋊#157

Splittings

Fitting, socle, HallC32×C5×C11 ⋊ C4
derived, HallC32×C11 ⋊ C4×C5
HallC5×C11 ⋊ #157
HallC32×C5 ⋊ Dic11
SylowC11 ⋊ C5×#157
SylowC32 ⋊ C5×Dic11

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#157
commutator, hypocenterC32×C11C4×C5
FrattiniC1G
Fitting, socleC32×C5×C11C4
prime radicalC5×C11×C3⋊D3C2
cosocleC11×C3⋊D3C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 330

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×C11⋊#157, C5×C7⋊(C11⋊#157), C5×C121⋊#157, …
maximal normal subgroup ofC5×C7×C11⋊#157, C5×C11×C11⋊#157, C5×C13×C11⋊#157, …
maximal quotient ofC5×C7×C11⋊#157, C5×C7⋊(C11⋊#157), C5×C121⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 80);