Finite Group Databasebeta

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C3×C29×D77 #27211518

order13398
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×D77
unambiguous semidirect productC11⋊(C3×D7×C29)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, HallC7×C11 ⋊ C2×C3×C29
HallC7×C11×C29 ⋊ C2×C3
HallC3×C11×C29 ⋊ D7
HallC3×C7×C29 ⋊ D11
HallC11×C29 ⋊ C3×D7
HallC3×C7×C11 ⋊ C2×C29
HallC7×C29 ⋊ C3×D11
HallC3×C11 ⋊ D7×C29
HallC3×C7 ⋊ D11×C29
SylowC11 ⋊ C3×D7×C29
SylowC7 ⋊ C3×D11×C29

Subgroups

subgroupG/H
center, hypercenterC3×C29D77
commutator, cosocle, hypocenterC7×C11C2×C3×C29
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C7×C11
UCSC1 ◁ C3×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)(8,9)(10,11)(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);(1,2,4,6,8,10,11,9,7,5,3)(12,13,15,17,18,16,14)

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D29×D77, C3×D7×D11×C29, C3×D77⋊D29, …
maximal normal subgroup ofC3×D29×D77, C3×D7×D11×C29, C3×D77⋊D29, …
maximal quotient ofC3×C29×Dic77, C2×C3×C29×D77

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 9);