Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C137 · Schur multiplier (H2) = C23 |
| direct product | C2×D64×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | D32 |
| commutator, Frattini, cosocle | C32 | C23×C137 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C4×C137 ◁ C2×C8×C137 ◁ C2×C16×C137 ◁ C2×C32×C137 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 203 |
| transitive degree | μt(G) = 17536 |
A minimal faithful permutation representation — 3 generators on 203 points:
(1,2)(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);(3,4)(5,10)(6,21)(7,25)(8,28)(9,15)(11,16)(12,17)(13,22)(14,26)(18,38)(19,40)(20,32)(23,56)(24,54)(27,58)(29,42)(30,41)(31,49)(33,48)(34,51)(35,44)(36,57)(37,47)(39,55)(43,59)(45,53)(46,52)(50,63)(60,66)(61,65)(62,64);(4,10)(5,16)(6,17)(7,22)(8,26)(11,12)(13,38)(14,40)(15,32)(18,48)(19,51)(20,44)(21,29)(23,57)(24,47)(25,30)(27,55)(28,31)(33,53)(34,52)(35,37)(36,59)(39,63)(41,42)(43,49)(45,46)(50,66)(54,61)(56,60)(58,62)(64,65)9590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 6726);