Finite Group Databasebeta

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C2×C11⋊(C11⋊(D7⋊C9)) #44478941

order30492
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C11⋊(C11⋊(D7⋊C9))
unambiguous semidirect product(C2×C11)⋊(C11⋊(D7⋊C9))
unambiguous semidirect product(C2×C7⋊C9)⋊(C11⋊D11)

Splittings

derived, HallC7×C112 ⋊ C22×C9
HallC112×C7⋊C9 ⋊ C22
HallC2×C7⋊(C11⋊D11) ⋊ C9
SylowC112 ⋊ C2×D7⋊C9
HallC7⋊C9 ⋊ C2×C11⋊D11
SylowC7 ⋊ C2×C9×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(C11⋊AGL(1,𝔽7))
commutator, hypocenterC7×C112C22×C9
FrattiniC3C2×C11⋊(C11⋊AGL(1,𝔽7))
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C7⋊(C11⋊D11)C3
cosocleC3×C7×C112C22×C3
LCSG ▷ C7×C112
UCSC1 ◁ C2×C3

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 15246

A minimal faithful permutation representation — 3 generators on 40 points:

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

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, 164);