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×#21132 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C101 | C22×D4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C22×C4 | C24×C101 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ #376×C101 ◁ G | |
814 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 25856 |
A minimal faithful permutation representation — 4 generators on 129 points:
(1,2,4,3)(5,6)(7,10)(8,9)(11,12)(13,14,19,24)(15,20,16,26)(17,23,18,22)(21,25,28,27)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(1,3,4,2)(6,9)(10,12)(13,15,19,16)(14,20,24,26)(17,27,18,25)(21,22,28,23);(13,16,19,15)(14,21,24,28)(17,27,18,25)(20,22,26,23);(5,7,8,11)(6,10,9,12)(13,17,19,18)(14,22,24,23)(15,25,16,27)(20,21,26,28)6464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 14120);