Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#12994 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C109 | C2×D8 |
| commutator | C2×C8 | C22×C4×C109 |
| Frattini, cosocle | C22×C8 | C23×C109 |
| prime radical | C24×C109 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C23×C4×C109 ◁ C23×C8×C109 ◁ G | |
530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 3 generators on 149 points:
(2,4)(5,6)(7,8)(9,10,14,19,29,38,27,36,15,20,13,18,12,17,28,37)(11,21,24,34,22,40,30,16,26,33,23,32,25,39,31,35)(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)(9,11)(10,16)(12,22)(13,30)(14,31)(15,26)(17,32)(18,39)(19,40)(20,35)(21,36)(23,27)(24,28)(25,29)(33,37)(34,38);(6,8)(9,12,15,29)(10,17,20,38)(11,22,26,25)(13,27,14,28)(16,32,35,34)(18,36,19,37)(21,40,33,39)(23,31,24,30)6322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 5982);