Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C113 · Schur multiplier (H2) = C25 |
| direct product | C113×#22527 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C113 | C22×D4 |
| commutator | C2×C4 | C23×C4×C113 |
| Frattini, cosocle | C22×C4 | C24×C113 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C2×C4×Q8×C113 ◁ G | |
990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 28928 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,3,4)(6,9)(10,11)(13,14)(15,22)(16,20)(17,25)(18,21)(19,24)(23,28)(26,27)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(5,6,8,9)(7,11,12,10)(15,23)(19,27)(22,28)(24,26);(13,15,18,23)(14,19,21,27)(16,24,17,26)(20,28,25,22);(5,7,8,12)(6,10,9,11)(13,16,18,17)(14,20,21,25)(15,24,23,26)(19,28,27,22)6554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 15515);