Finite Group DatabasebetaFinite Group Databasebeta| order | 38637 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C34 |
| direct product | C53×#10624656 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ C34×C53 ◁ G | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2,5)(3,9,14)(4,8,15)(6,16,12)(7,19,13)(10,21,24)(11,18,26)(17,27,23)(20,25,22)(28,29,32)(30,36,47)(31,35,42)(33,43,39)(34,46,40)(37,44,51)(38,45,41)(48,52,50)(49,53,54)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,10)(2,6,17)(4,12,22)(5,14,24)(7,9,20)(8,18,21)(11,23,13)(15,16,25)(19,26,27)(28,30,37)(29,33,44)(31,39,49)(32,41,51)(34,36,48)(35,45,53)(38,50,40)(42,47,54)(43,52,46);(2,7,8)(3,11,12)(5,15,19)(6,18,9)(10,22,23)(24,27,25)(29,34,35)(32,42,46)(33,36,45)(41,47,43)(44,48,53)(51,54,52)2173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38637, 216);