Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#32701 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C109 |
| prime radical | #534×C109 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C24×C109 ◁ G | |
628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2)(3,11,14,7)(4,15,18,8)(5,9)(6,10)(12,25)(13,21,27,23)(16,20)(17,28,30,22)(19,24)(26,31)(29,32)(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);(1,3)(2,7)(4,16)(5,13)(6,14)(8,20)(9,23)(10,11)(12,18)(15,25)(17,29)(19,27)(21,24)(22,32)(26,30)(28,31);(1,4)(2,8)(3,12,14,16)(5,17)(6,18)(7,20,11,25)(9,22)(10,15)(13,26,27,29)(19,30)(21,31,23,32)(24,28);(1,5,6,19)(2,9,10,24)(3,13,14,27)(4,17,18,30)(7,21,11,23)(8,22,15,28)(12,26,16,29)(20,31,25,32)3706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25689);