Finite Group Databasebeta

← Prev (#27211515) Next (#27211517) →

C3×C11×D7×C29 #27211516

order13398
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D7×C29

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, SylowC7 ⋊ C2×C3×C11×C29
HallC7×C11×C29 ⋊ C2×C3
HallC3×C7×C29 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C29
HallC7×C29 ⋊ C2×C3×C11
HallC7×C11 ⋊ C2×C3×C29
HallC3×C7 ⋊ C2×C11×C29

Subgroups

subgroupG/H
center, hypercenterC3×C11×C29D7
commutator, cosocle, hypocenterC7C2×C3×C11×C29
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C7
UCSC1 ◁ C3×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)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47)(48,49,50);(1,2,4,6,7,5,3)

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D7×D29, C3×D7×D11×C29, C3×D7×D319, …
maximal normal subgroup ofC3×C11×D7×D29, C3×D7×D11×C29, C3×D7×D319, …
maximal quotient ofC3×C11×Dic7×C29, C2×C3×C11×D7×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 7);