Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C24 |
| direct product | C151×#13356 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C151 |
| prime radical | #585×C151 | C22 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×#41×C151 ◁ G | |
676 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 215 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 215 points:
(1,2,7,12)(3,13,17,35)(4,18,21,37)(5,22,25,10)(6,26,28,11)(8,23,31,15)(9,27,34,20)(14,40,43,64)(16,46,48,39)(19,51,53,50)(24,36,58,55)(29,60,32,63)(30,45,59,56)(33,52,54,57)(38,47,61,42)(41,49,44,62)(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);(1,3)(2,8)(4,14)(5,23)(6,16)(7,17)(9,32)(10,35)(11,30)(12,31)(13,22)(15,25)(18,49)(19,44)(20,42)(21,43)(24,56)(26,59)(27,47)(28,48)(29,34)(33,61)(36,46)(37,62)(38,54)(39,55)(40,51)(41,53)(45,58)(50,64)(52,63)(57,60);(1,4,7,21)(2,9,12,34)(3,14,17,43)(5,19,25,53)(6,27,28,20)(8,29,31,32)(10,33,22,54)(11,37,26,18)(13,38,35,61)(15,44,23,41)(16,47,48,42)(24,57,58,52)(30,49,59,62)(36,51,55,50)(39,64,46,40)(45,60,56,63)4228 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6344);