Finite Group DatabasebetaFinite Group Databasebeta| order | 13398 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊(D29⋊C7)) |
| unambiguous semidirect product | C11⋊(C3⋊(D29⋊C7)) |
| unambiguous semidirect product | (C29⋊C7)⋊D33 |
| unambiguous semidirect product | D957⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C29 | C2×C7 |
| LCS | G ▷ C3×C11×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 957 |
A minimal faithful permutation representation — 2 generators on 43 points:
(2,6,7,21,14,22,28,3,4,11,13,20,26,29)(5,18,19,23,24,15,16,9,10,27,12,25,8,17)(31,32)(33,34)(35,36)(37,38)(39,40)(42,43);(1,2,5,10,20,11,22,13,25,29,27,16,15,6,12,23,4,8,17,19,28,24,21,26,7,14,18,9,3)(30,31,33,35,37,39,40,38,36,34,32)(41,42,43)Polycyclic presentation:
2,3,7,11,29|b^a=b^2,d^a=d^10,e^a=e^28,e^c=e^16192 conjugacy classes — view the full character table.
| maximal subgroup of | D33×D29⋊C7, D11×C3⋊(D29⋊C7), D3×C11⋊(D29⋊C7), … |
| maximal normal subgroup of | D33×D29⋊C7, D11×C3⋊(D29⋊C7), D3×C11⋊(D29⋊C7), … |
| maximal quotient of | C3⋊(C11⋊(Dic29⋊C7)), C2×C3⋊(C11⋊(D29⋊C7)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13398, 25);