Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C113 · Schur multiplier (H2) = C22×C4 |
| direct product | C113×#13250 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #442 |
| commutator | C2×C8 | C22×C4×C113 |
| Frattini, cosocle | C22×C8 | C23×C113 |
| prime radical | C2×#135×C113 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C22×C4×C113 ◁ C2×#97×C113 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 3 generators on 149 points:
(2,4)(5,6)(7,17,20,33)(8,21,24,34)(9,25)(10,27)(11,16)(12,19,30,26)(13,23,31,35)(14,18)(15,28)(22,29)(32,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(1,2,3,4)(5,7,18,35,28,24,9,26,11,20,36,23,10,8,22,19)(6,12,25,21,27,13,14,33,16,30,29,34,15,31,32,17);(5,8,22,35,10,20,36,19,11,24,9,23,28,7,18,26)(6,13,32,34,15,12,29,33,16,31,14,21,27,30,25,17)3842 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 6238);