Finite Group DatabasebetaFinite Group Databasebeta| order | 25216 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C197 · Schur multiplier (H2) = C22 |
| direct product | C2×M64×C197 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C197 | C22 |
| commutator | C2 | C22×C16×C197 |
| Frattini, cosocle | C16 | C23×C197 |
| socle | C22×C197 | C2×C16 |
| prime radical | C23×C197 | C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C197 ◁ G | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 231 |
| transitive degree | μt(G) = 12608 |
A minimal faithful permutation representation — 3 generators on 231 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231);(3,4,5,10,6,11,13,22,7,12,14,23,16,24,25,32,8,9,15,19,17,20,26,29,18,21,27,30,28,31,33,34);(4,9)(10,19)(11,20)(12,21)(22,29)(23,30)(24,31)(32,34)15760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25216, 989);