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C3×D2233 #27211519

order13398
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D2233
unambiguous semidirect productC11⋊(C3×D203)
unambiguous semidirect productC29⋊(C3×D77)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, HallC7×C11×C29 ⋊ C2×C3
HallC3×C11×C29 ⋊ D7
HallC3×C7×C29 ⋊ D11
HallC11×C29 ⋊ C3×D7
HallC3×C7×C11 ⋊ D29
HallC7×C29 ⋊ C3×D11
HallC3×C29 ⋊ D77
HallC7×C11 ⋊ C3×D29
HallC3×C11 ⋊ D203
SylowC29 ⋊ C3×D77
HallC3×C7 ⋊ D319
SylowC11 ⋊ C3×D203
SylowC7 ⋊ C3×D319

Subgroups

subgroupG/H
center, hypercenterC3D2233
commutator, cosocle, hypocenterC7×C11×C29C2×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C7×C11×C29
UCSC1 ◁ C3

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)(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)(30,31,33,35,37,39,40,38,36,34,32)(41,42,44,46,47,45,43)

Conjugacy classes & character table

3354 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D29×D77, C3×D11×D203, C3×D7×D319, …
maximal normal subgroup ofC3×D29×D77, C3×D11×D203, C3×D7×D319, …
maximal quotient ofC3×Dic2233, C2×C3×D2233

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 10);