Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#19365 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C109 |
| prime radical | #121×C109 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G | |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2)(3,11)(4,10)(5,7)(6,9)(8,12)(13,16)(14,15)(17,18,22,24)(19,21,26,31)(20,27,30,25)(23,29,32,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(2,7)(8,15)(9,10)(11,16)(17,19,21,24,22,26,31,18)(20,25,29,32,30,27,28,23);(1,3)(2,8)(4,12)(5,13)(6,14)(7,15)(9,11)(10,16)(17,20)(18,23)(19,25)(21,29)(22,30)(24,32)(26,27)(28,31);(1,4,5,6)(2,9,7,10)(3,12,13,14)(8,11,15,16)(17,21,22,31)(18,19,24,26)(20,28,30,29)(23,27,32,25)4360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 12353);