Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C36 |
| direct product | C37×#10624894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C32×H(3,𝔽3)×C37 | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ G | |
1148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 4 generators on 73 points:
(1,2,4)(3,6,8)(5,9,7)(10,11,14,13,16,23,21,27,34)(12,17,28,20,26,22,19,15,24)(18,30,35,31,25,36,32,29,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(10,12,18)(11,15,25)(13,20,31)(14,22,33)(16,17,29)(19,32,21)(23,24,35)(26,30,27)(28,36,34);(2,5,6)(4,8,9);(12,19,20)(15,26,17)(18,31,32)(22,28,24)(25,29,30)(33,35,36)4477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 454);