Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C109 · Schur multiplier (H2) = C23 |
| direct product | C109×#9268 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #386 |
| commutator | C22×C4 | C22×C4×C109 |
| Frattini, cosocle | C2×C42 | C23×C109 |
| prime radical | C23×C109 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 3 generators on 141 points:
(2,6)(3,9)(4,12)(8,14)(10,11)(13,15)(17,18,21,23,22,26,20,25)(19,27,29,24,30,31,28,32)(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);(1,2,4,6,5,8,12,14)(3,7,10,13,11,16,9,15)(18,23)(20,21)(24,27)(25,26)(28,29)(31,32);(1,3)(2,7)(4,10)(5,11)(6,13)(8,16)(9,12)(14,15)(17,19,22,30)(18,24,26,32)(20,29,21,28)(23,27,25,31)4687 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 2256);