Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C24 |
| direct product | C151×#13312 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C151 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C151 |
| socle | C2×C151 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G | |
520 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 114 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)(3,15)(4,21)(5,26)(6,13)(7,12)(8,14)(9,17)(10,24)(11,29)(16,45)(18,51)(19,39)(20,44)(22,54)(23,56)(25,37)(27,42)(28,41)(30,40)(31,38)(32,61)(33,49)(34,50)(35,46)(36,59)(43,47)(48,64)(52,55)(53,58)(57,62)(60,63)(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)(2,9)(4,22)(5,27)(6,18)(7,19)(8,20)(10,35)(11,39)(12,33)(13,42)(14,34)(15,26)(16,24)(17,29)(21,52)(23,57)(25,47)(28,50)(30,49)(31,48)(32,37)(36,43)(38,62)(40,44)(41,51)(45,53)(46,59)(54,56)(55,58)(60,61)(63,64);(1,4)(2,10)(3,16)(5,23)(6,31)(7,24)(8,25)(9,32)(11,36)(12,37)(13,21)(14,38)(15,43)(17,46)(18,22)(19,47)(20,48)(26,53)(27,55)(28,60)(29,58)(30,59)(33,62)(34,52)(35,42)(39,64)(40,63)(41,56)(44,54)(45,51)(49,61)(50,57)6040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 6300);