Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C109 · Schur multiplier (H2) = C26 |
| direct product | C109×#21776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2308 |
| commutator | C23 | C23×C4×C109 |
| Frattini, cosocle | C24 | C24×C109 |
| prime radical | C109×#3484 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C24×C109 ◁ G | |
1520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 1744 |
A minimal faithful permutation representation — 4 generators on 125 points:
(1,2)(3,9,11,6)(4,12,13,7)(5,8)(10,14)(15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(1,3)(2,6)(4,10)(5,11)(7,14)(8,9)(12,15)(13,16);(6,9)(14,15);(1,4)(2,7)(3,10)(5,13)(6,14)(8,12)(9,15)(11,16)5014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 14764);