Finite Group DatabasebetaFinite Group Databasebeta| order | 38144 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C149 · Schur multiplier (H2) = C2 |
| direct product | C149×#13108 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C149 | #387 |
| commutator | C22×C4 | C22×C4×C149 |
| Frattini, cosocle | C22×C8 | C23×C149 |
| socle | C2×C149 | #1917 |
| prime radical | C23×C149 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C149 ◁ C22×C8×C149 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 4768 |
A minimal faithful permutation representation — 3 generators on 181 points:
(1,2,6,13,7,11,25,30,8,12,26,14,5,21,23,17)(3,4,10,20,15,9,27,28,16,19,29,24,22,18,32,31)(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);(1,3,6,10,7,15,25,27,8,16,26,29,5,22,23,32)(2,9,13,28,11,19,30,24,12,18,14,31,21,4,17,20);(1,4,5,18,8,19,7,9)(2,10,11,27,12,29,21,32)(3,14,15,17,16,13,22,30)(6,24,23,28,26,20,25,31)6854 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38144, 6096);