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C3×C11×D203 #27211517

order13398
isoclinismisoclinic class of D203
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D203
unambiguous semidirect productC29⋊(C3×C11×D7)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, HallC7×C29 ⋊ C2×C3×C11
HallC7×C11×C29 ⋊ C2×C3
HallC3×C11×C29 ⋊ D7
HallC3×C7×C29 ⋊ C2×C11
HallC11×C29 ⋊ C3×D7
HallC3×C7×C11 ⋊ D29
HallC3×C29 ⋊ C11×D7
HallC7×C11 ⋊ C3×D29
SylowC29 ⋊ C3×C11×D7
HallC3×C7 ⋊ C11×D29
SylowC7 ⋊ C3×C11×D29

Subgroups

subgroupG/H
center, hypercenterC3×C11D203
commutator, cosocle, hypocenterC7×C29C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C7×C29
UCSC1 ◁ C3×C11

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

Conjugacy classes & character table

3399 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D7×D29, C3×D11×D203, C3×D77⋊D29, …
maximal normal subgroup ofC3×C11×D7×D29, C3×D11×D203, C3×D77⋊D29, …
maximal quotient ofC3×C11×Dic203, C2×C3×C11×D203

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 8);