Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C113 · Schur multiplier (H2) = C25 |
| direct product | C113×#25145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C113 |
| prime radical | C113×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 4 generators on 149 points:
(1,2)(3,4)(5,6,11,24,10,15,9,14)(7,12,25,36,18,28,17,27)(8,19,21,13,23,30,22,31)(16,32,33,26,20,35,34,29)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(2,4)(5,7,9,17,10,18,11,25)(6,12,14,27,15,28,24,36)(8,20,22,33,23,16,21,34)(13,29,19,35,31,26,30,32);(5,8)(6,13)(7,16)(9,21)(10,23)(11,22)(12,26)(14,30)(15,31)(17,33)(18,20)(19,24)(25,34)(27,35)(28,29)(32,36);(2,4)(5,9,10,11)(6,14,15,24)(7,17,18,25)(8,21,23,22)(12,27,28,36)(13,30,31,19)(16,33,20,34)(26,35,29,32)4859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 18133);