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C5×C11×#157 #14520454

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

Aliases

direct productC5×C11×#157

Splittings

Fitting, socle, HallC32×C5×C11 ⋊ C4
derived, SylowC32 ⋊ C4×C5×C11
HallC32×C11 ⋊ C4×C5
HallC32×C5 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11#157
commutator, hypocenterC32C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11C4
prime radicalC5×C11×C3⋊D3C2
cosocleC3⋊D3C2×C5×C11
LCSG ▷ C32
UCSC1 ◁ C5×C11

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C7×C11×#157, C5×C11×C7⋊#157, C5×#157×C121, …
maximal normal subgroup ofC5×C7×C11×#157, C5×#157×C121, C5×C112×#157, …
maximal quotient ofC5×C7×C11×#157, C5×C11×C7⋊#157, C5×#157×C121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 79);