Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C28 |
| direct product | C109×#32895 |
| 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 | |
3540 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 4 generators on 141 points:
(2,8)(3,12)(5,6)(10,25)(11,17)(13,27)(14,19)(15,18)(20,23)(21,26)(22,31)(28,29)(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)(3,9)(4,10)(5,17)(6,8)(7,11)(12,23)(13,22)(14,24)(15,21)(16,26)(18,25)(19,20)(27,32)(28,30)(29,31);(1,3,7,14)(2,9,11,24)(4,13,16,29)(5,12,6,19)(8,20,17,23)(10,22,26,31)(15,28,18,27)(21,30,25,32);(1,4)(2,10)(3,13)(5,18)(6,15)(7,16)(8,21)(9,22)(11,26)(12,27)(14,29)(17,25)(19,28)(20,30)(23,32)(24,31)5014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 25883);