Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C113 · Schur multiplier (H2) = C23 |
| direct product | C113×#10188 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C113 |
| prime radical | C113×#3036 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 3 generators on 137 points:
(1,2,4,7)(3,5,8,6)(9,10)(11,19)(12,17)(13,16)(14,18)(15,20)(21,24)(22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(2,5)(3,8)(6,7)(9,11)(10,15)(12,21)(13,20)(14,22)(16,23)(17,19)(18,24);(10,16)(11,20)(12,13)(17,18)(19,23)(21,22)4181 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 3176);