Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#13670 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C151 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C2×C4×C151 ◁ #131×C151 ◁ #504×C151 ◁ G | |
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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:
(2,9)(3,14)(4,18)(5,7)(6,20)(10,32)(11,37)(12,38)(13,31)(15,42)(16,46)(17,24)(19,26)(21,49)(22,48)(23,50)(25,27)(28,30)(29,33)(34,43)(35,57)(36,56)(39,53)(40,44)(45,63)(47,58)(51,55)(52,62)(59,61)(60,64)(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);(1,2)(3,10)(4,19)(5,11)(6,26)(7,28)(8,13)(9,18)(12,20)(14,33)(15,43)(16,47)(17,36)(21,38)(22,53)(23,51)(24,35)(25,39)(27,55)(29,44)(30,48)(31,50)(32,42)(34,41)(37,49)(40,58)(45,64)(46,59)(52,61)(54,60)(56,63)(57,62);(1,3,8,17)(2,10,13,36)(4,15,23,45)(5,24,7,14)(6,16,27,46)(9,29,31,57)(11,35,28,33)(12,34,39,60)(18,44,50,62)(19,43,51,64)(20,41,25,54)(21,52,22,40)(26,47,55,59)(30,56,37,32)(38,61,53,58)(42,48,63,49)5587 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6658);