Finite Group Databasebeta

← Prev (#44479147) Next (#44479149) →

C2×C3×C11⋊(C11⋊AGL(1,𝔽7)) #44479148

order30492
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C11

Aliases

direct productC2×C3×C11⋊(C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×C11)⋊(C3×C11⋊AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C3×C11⋊D11)

Splittings

Fitting, socleC2×C3×C7×C112 ⋊ C2×C3
derived, HallC7×C112 ⋊ C22×C32
HallC3×C112×ΓL(1,𝔽8) ⋊ C22
HallC2×C7⋊(C11⋊D11) ⋊ C32
SylowC112 ⋊ C2×C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C2×C11⋊D11
SylowC7 ⋊ C2×C32×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(C11⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC7×C112C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C112C2×C3
LCSG ▷ C7×C112
UCSC1 ◁ C2×C3

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 5082

A minimal faithful permutation representation — 3 generators on 34 points:

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

Conjugacy classes & character table

1842 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 371);