Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C28 |
| direct product | C109×#32894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
3638 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)(3,14)(4,10)(5,12)(6,11)(7,13)(8,16)(9,18)(15,22)(17,27)(19,26)(20,24)(21,25)(23,30)(28,31)(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)(2,8)(4,15)(5,20)(6,16)(7,17)(9,22)(10,23)(11,27)(12,14)(13,24)(18,31)(19,32)(21,30)(25,29)(26,28);(1,4)(2,9)(3,15)(5,18)(6,21)(7,19)(8,22)(10,11)(12,26)(13,25)(14,28)(16,30)(17,32)(20,31)(23,27)(24,29);(1,4)(2,10)(3,15)(5,21)(6,18)(7,19)(8,23)(9,11)(12,25)(13,26)(14,29)(16,31)(17,32)(20,30)(22,27)(24,28)5014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25882);