Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C151 · Schur multiplier (H2) = C25 |
| direct product | C151×#12684 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C151 | #120 |
| commutator | C23 | C22×C8×C151 |
| Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C2×C151 | #1779 |
| prime radical | #585×C151 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C151 ◁ C22×C8×C151 ◁ G | |
894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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:
(1,2,5,10,6,11,20,30,7,12,21,31,22,32,43,53)(3,8,15,25,16,26,39,49,14,24,37,47,38,48,58,62)(4,9,18,28,19,29,42,52,17,27,40,50,41,51,59,63)(13,33,35,54,36,55,57,64,34,23,44,45,56,46,60,61)(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)(4,13)(5,15)(6,16)(7,14)(9,23)(10,25)(11,26)(12,24)(17,34)(18,35)(19,36)(20,39)(21,37)(22,38)(27,33)(28,45)(29,46)(30,49)(31,47)(32,48)(40,44)(41,56)(42,57)(43,58)(50,54)(51,55)(52,61)(53,62)(59,60)(63,64);(1,4)(2,9)(3,13)(5,18)(6,19)(7,17)(8,23)(10,28)(11,29)(12,27)(14,34)(15,35)(16,36)(20,42)(21,40)(22,41)(24,33)(25,45)(26,46)(30,52)(31,50)(32,51)(37,44)(38,56)(39,57)(43,59)(47,54)(48,55)(49,61)(53,63)(58,60)(62,64)9664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5672);