Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C197 · Schur multiplier (H2) = C29 |
| direct product | #3573×C197 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C197 | C24 |
| commutator | C2 | C24×C4×C197 |
| Frattini, cosocle | C4 | C25×C197 |
| socle | C2×C197 | C24×C4 |
| prime radical | #585×C197 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C197 ◁ G | |
1424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 229 |
| transitive degree | μt(G) = 6304 |
A minimal faithful permutation representation — 5 generators on 229 points:
(1,2,5,9,6,10,16,22)(3,7,13,19,12,18,25,29)(4,8,15,21,14,20,26,30)(11,17,24,28,23,27,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229);(1,3)(2,7)(4,11)(5,13)(6,12)(8,17)(9,19)(10,18)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32);(1,4)(2,8)(3,11)(5,15)(6,14)(7,17)(9,21)(10,20)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32);(4,14)(8,20)(11,23)(15,26)(17,27)(21,30)(24,31)(28,32);(3,12)(7,18)(11,23)(13,25)(17,27)(19,29)(24,31)(28,32)13396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 2305);