Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C109 · Schur multiplier (H2) = C28 |
| direct product | C2×C109×#1794 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C109 | #120 |
| commutator | C2×C4 | C23×C4×C109 |
| Frattini, cosocle | C22×C4 | C24×C109 |
| socle | C22×C109 | #379 |
| prime radical | C2×#585×C109 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C109 ◁ C23×C4×C109 ◁ G | |
3662 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);(3,4,8,12,9,13,7,20)(5,14,16,10,17,25,21,24)(6,11,18,27,19,28,22,26)(15,30,33,34,32,29,31,23);(3,5)(4,10)(6,15)(7,21)(8,16)(9,17)(11,23)(12,25)(13,24)(14,20)(18,33)(19,32)(22,31)(26,29)(27,30)(28,34);(3,6)(4,11)(5,15)(7,22)(8,18)(9,19)(10,23)(12,27)(13,28)(14,29)(16,33)(17,32)(20,26)(21,31)(24,34)(25,30)6976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 13607);