Finite Group DatabasebetaFinite Group Databasebeta| order | 26598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#14559030 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C31 | C2×C3 |
| LCS | G ▷ C11×C13×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 4433 |
A minimal faithful permutation representation — 2 generators on 55 points:
(2,6,7,3,4,8)(5,14,15,9,10,22)(11,24,25,17,18,30)(12,23,19,20,16,13)(21,31,28,27,26,29)(33,37,38,34,35,39)(36,43,42,40,41,44)(46,47)(48,49)(50,51)(52,53)(54,55);(1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3)(32,33,36,35,39,42,41,43,44,38,37,40,34)(45,46,48,50,52,54,55,53,51,49,47)Polycyclic presentation:
2,3,11,13,31|c^a=c^10,d^a=d^12,e^a=e^30,d^b=d^3,e^b=e^25758 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26598, 47);