Finite Group Databasebeta

← Prev (#43249771) Next (#43249773) →

C2×C9⋊(D113⋊C7) #43249772

order28476
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9⋊(D113⋊C7)
unambiguous semidirect product(C2×C9)⋊(D113⋊C7)
unambiguous semidirect product(C2×C113⋊C7)⋊D9
unambiguous semidirect product(C2×D1017)⋊C7

Splittings

FittingC2×C9×C113 ⋊ C2×C7
derived, HallC9×C113 ⋊ C22×C7
HallC9×C113⋊C7 ⋊ C22
HallC2×D1017 ⋊ C7
HallC113⋊C7 ⋊ C2×D9
SylowC113 ⋊ C2×C7×D9
SylowC9 ⋊ C2×D113⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(D113⋊C7)
commutator, cosocle, hypocenterC9×C113C22×C7
FrattiniC3C2×C3⋊(D113⋊C7)
FittingC2×C9×C113C2×C7
socleC2×C3×C113D3×C7
LCSG ▷ C9×C113
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 124
transitive degreeμt(G) = 2034

A minimal faithful permutation representation — 2 generators on 124 points:

(4,6)(5,9)(7,8)(10,11)(13,17,18,36,41,35,44,14,15,23,25,61,58,59)(16,30,31,84,32,86,87,20,21,51,52,53,54,83)(19,45,46,107,110,64,75,27,28,76,78,121,95,96)(22,56,43,24,65,66,118,33,34,26,38,39,89,98)(29,55,81,97,106,99,82,48,49,88,113,74,67,50)(37,90,57,80,108,60,112,62,63,47,91,77,92,93)(40,100,101,124,123,109,117,68,69,114,120,111,122,115)(42,102,105,70,71,104,85,72,73,119,103,94,79,116);(1,2)(3,11,6,9,8,7,5,4,10)(12,13,16,22,35,60,94,61,86,78,111,121,66,49,53,30,25,42,74,93,91,39,67,98,105,113,95,62,18,26,44,75,52,63,34,57,45,77,109,120,101,88,73,100,46,79,103,68,38,15,19,29,50,83,115,116,31,51,85,117,87,82,48,27,17,24,40,70,104,76,69,102,81,114,124,122,108,28,47,56,90,84,96,59,43,23,37,64,97,119,118,99,65,80,112,106,72,36,21,32,55,89,110,123,107,54,41,71,92,58,33,20,14)

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 23);