Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C34 |
| direct product | C37×#10624910 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C37×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ G | |
740 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5,4,8,15,13,7,18)(3,9,20,11,19,14,12,6,16)(10,22,26,24,17,27,23,21,25)(28,29,32)(30,33,40)(31,35,41)(34,45,39)(36,42,48)(37,44,52)(38,43,49)(46,51,54)(47,50,53)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,10)(2,6,17)(4,11,24)(5,14,25)(7,19,22)(8,9,21)(12,23,13)(15,16,26)(18,20,27)(28,30,36)(29,33,42)(31,38,46)(32,40,48)(34,44,50)(35,43,51)(37,47,39)(41,49,54)(45,52,53);(3,11,12)(6,9,19)(10,23,24)(14,16,20)(17,22,21)(25,27,26)(29,34,35)(30,37,38)(32,41,45)(33,43,44)(36,46,47)(48,53,54);(2,7,8)(3,12,11)(5,15,18)(6,9,19)(10,24,23)(25,27,26)(29,34,35)(32,41,45)(33,44,43)(40,49,52)(42,50,51)(48,54,53)3293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 470);