Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C109 · Schur multiplier (H2) = C26 |
| direct product | C2×C109×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #381 |
| commutator | C23 | C23×C4×C109 |
| Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C24×C109 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G | |
1218 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 6976 |
A minimal faithful permutation representation — 4 generators on 143 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143);(3,4,7,12,8,11,21,26)(5,13,15,27,16,9,20,23)(6,17,19,31,18,10,24,25)(14,22,30,33,29,28,32,34);(3,5,8,16)(4,9,11,13)(6,14,18,29)(7,20,21,15)(10,22,17,28)(12,27,26,23)(19,32,24,30)(25,34,31,33);(3,6)(4,10,11,17)(5,14)(7,19)(8,18)(9,22,13,28)(12,25,26,31)(15,30)(16,29)(20,32)(21,24)(23,33,27,34)6322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 13700);