Finite Group Databasebeta

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C11×C29×D21 #27211524

order13398
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC11×C29×D21
unambiguous semidirect productC3⋊(C11×D7×C29)
unambiguous semidirect productC7⋊(D3×C11×C29)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, HallC3×C7 ⋊ C2×C11×C29
HallC7×C11×C29 ⋊ D3
HallC3×C11×C29 ⋊ D7
HallC3×C7×C29 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C29
HallC7×C29 ⋊ D3×C11
HallC3×C29 ⋊ C11×D7
HallC7×C11 ⋊ D3×C29
HallC3×C11 ⋊ D7×C29
SylowC7 ⋊ D3×C11×C29
SylowC3 ⋊ C11×D7×C29

Subgroups

subgroupG/H
center, hypercenterC11×C29D21
commutator, cosocle, hypocenterC3×C7C2×C11×C29
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C3×C7
UCSC1 ◁ C11×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 6699

A minimal faithful permutation representation — 2 generators on 50 points:

(2,3)(4,5)(6,7)(9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50);(1,2,4,6,7,5,3)(8,9,10)

Conjugacy classes & character table

3828 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D21×D29, D11×C29×D21, D21×D319, …
maximal normal subgroup ofC11×D21×D29, D11×C29×D21, D21×D319, …
maximal quotient ofC11×C29×Dic21, C2×C11×C29×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 15);