Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C101 · Schur multiplier (H2) = C23×C8 |
| direct product | C101×#19724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C101 |
| prime radical | C101×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2)(3,11)(4,8)(5,9)(6,16)(7,10)(12,14)(13,15)(17,18)(19,25)(20,30)(21,26)(22,31)(23,27)(24,28)(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);(1,3,6,8,7,13,5,12)(2,4,9,11,10,14,16,15)(17,19,22,28,23,29,21,20)(18,24,26,25,27,30,31,32);(1,4,7,14)(2,8,10,12)(3,9,13,16)(5,15,6,11)(17,20,21,29,23,28,22,19)(18,25,31,24,27,32,26,30);(1,5,7,6)(2,9,10,16)(3,12,13,8)(4,11,14,15)(17,21,23,22)(18,26,27,31)(19,28,29,20)(24,32,30,25)4040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 12712);