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C7×C3⋊(C3⋊(C11⋊D11)) #29503902

order15246
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3×C11

Aliases

direct productC7×C3⋊(C3⋊(C11⋊D11))
unambiguous semidirect productC3⋊(C7×C3⋊(C11⋊D11))
unambiguous semidirect productC11⋊(C7×C3⋊D33)

Splittings

Fitting, socle, HallC32×C7×C112 ⋊ C2
derived, HallC32×C112 ⋊ C2×C7
HallC7×C112 ⋊ C3⋊D3
SylowC112 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ C11⋊D11
SylowC32 ⋊ C7×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊(C11⋊D11))
commutator, cosocle, hypocenterC32×C112C2×C7
FrattiniC1G
Fitting, socleC32×C7×C112C2
LCSG ▷ C32×C112
UCSC1 ◁ C7

336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 7623

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(34,35);(19,20,22,24,26,28,29,27,25,23,21)(33,34,35);(8,9,11,13,15,17,18,16,14,12,10)(30,31,32)

Conjugacy classes & character table

3822 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×#17983787, C7⋊#17983787, C7×D332, …
maximal normal subgroup ofC7×#17983787, C7⋊#17983787, C7×D332, …
maximal quotient ofC7×C3⋊(C3⋊(C11⋊Dic11)), C2×C7×C3⋊(C3⋊(C11⋊D11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15246, 103);