Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C23×C4 |
| direct product | C101×#20788 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C101 | C2×#117 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| socle | C2×C101 | #2283 |
| prime radical | C2×#41×C101 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C101 ◁ #405×C101 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 points:
(1,2)(3,12,15,8)(4,9)(5,10)(6,11)(7,14,21,29)(13,27,16,22)(17,24)(18,25)(19,26)(20,28,23,30)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3)(2,7,11,21)(4,16)(5,14)(6,15)(8,10,12,26)(9,23,25,20)(13,18)(17,30)(19,29)(22,32,27,24)(28,31);(1,3)(2,8)(4,13)(5,14)(6,15)(7,10)(9,22)(11,12)(16,18)(17,28)(19,29)(20,24)(21,26)(23,32)(25,27)(30,31);(1,4,5,17,6,18,19,31)(2,9,10,24,11,25,26,32)(3,13,14,28,15,16,29,30)(7,20,12,27,21,23,8,22)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 13776);