Finite Group DatabasebetaFinite Group Databasebeta| order | 38656 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C23 |
| direct product | C151×#12118 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C151 |
| prime radical | #2017×C151 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×M16×C151 ◁ G | |
392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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)(4,20)(5,24)(6,13)(7,12)(8,14)(9,17)(10,22)(11,27)(16,44)(18,52)(19,43)(21,55)(23,40)(25,33)(26,36)(28,41)(29,37)(30,39)(31,38)(32,59)(34,50)(35,51)(42,46)(45,53)(47,64)(48,62)(49,60)(54,58)(56,61)(57,63)(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);(1,3,8,19)(2,9,14,35)(4,16,23,48)(5,25,28,50)(6,18,7,31)(10,32,37,61)(11,38,39,52)(12,34,13,33)(15,41,43,24)(17,30,51,27)(20,53,40,60)(21,56,26,59)(22,46,29,47)(36,62,55,44)(42,63,64,54)(45,57,49,58);(1,4)(2,10)(3,16)(5,26)(6,29)(7,22)(8,23)(9,32)(11,36)(12,40)(13,20)(14,37)(15,42)(17,49)(18,47)(19,48)(21,28)(24,54)(25,59)(27,57)(30,58)(31,46)(33,53)(34,60)(35,61)(38,62)(39,55)(41,63)(43,64)(44,52)(45,51)(50,56)3775 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38656, 5106);