Finite Group DatabasebetaFinite Group Databasebeta| order | 21875 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C252 · Schur multiplier (H2) = C5 |
| direct product | C7×#15691073 |
| subgroup | G/H | |
|---|---|---|
| center | C5×C7×C25 | C52 |
| commutator | C5 | C7×C252 |
| Frattini, cosocle | C5×C25 | C52×C7 |
| socle, prime radical | C52×C7 | C5×C25 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C7×C25 ◁ G | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 157 |
| transitive degree | μt(G) = 21875 |
A minimal faithful permutation representation — 2 generators on 157 points:
(26,27,30,37,51,28,32,39,53,73,34,44,57,76,97,47,64,81,100,119,67,89,105,122,137,29,33,40,54,72,35,45,58,77,96,48,65,82,101,118,68,90,106,123,136,92,113,127,140,147,36,46,59,52,74,49,66,83,75,98,69,91,107,99,120,93,114,128,121,138,115,133,143,139,148,50,42,38,55,78,70,62,56,79,102,94,87,80,103,124,116,111,104,125,141,134,132,126,142,149,71,31,41,60,84,95,43,61,85,108,117,63,86,109,129,135,88,110,130,144,146,112,131,145,150)(151,152,153,154,155,156,157);(1,2,4,7,11,3,5,8,12,16,6,9,13,17,20,10,14,18,21,23,15,19,22,24,25)(27,31,42,46,33)(30,38,40,41,59)(32,43,62,66,45)(37,52,60,54,55)(39,56,58,61,83)(44,63,87,91,65)(51,72,74,78,84)(53,75,85,77,79)(57,80,82,86,107)(64,88,111,114,90)(73,96,98,102,108)(76,99,109,101,103)(81,104,106,110,128)(89,112,132,133,113)(97,118,120,124,129)(100,121,130,123,125)(105,126,127,131,143)(119,136,138,141,144)(122,139,145,140,142)(137,147,148,149,150)5075 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21875, 16);