Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 7 |
| isoclinism | isoclinic class of D128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×SD256 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | D64 |
| commutator, Frattini, cosocle | C64 | C22×C17 |
| prime radical | C17×D64 | C2 |
| LCS | G ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C4×C17 ◁ C8×C17 ◁ C16×C17 ◁ C17×C32 ◁ C17×C64 ◁ G | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 145 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(19,81)(20,144)(21,79)(22,142)(23,77)(24,140)(25,75)(26,138)(27,73)(28,136)(29,71)(30,134)(31,69)(32,132)(33,67)(34,130)(35,65)(36,128)(37,63)(38,126)(39,61)(40,124)(41,59)(42,122)(43,57)(44,120)(45,55)(46,118)(47,53)(48,116)(49,51)(50,114)(52,112)(54,110)(56,108)(58,106)(60,104)(62,102)(64,100)(66,98)(68,96)(70,94)(72,92)(74,90)(76,88)(78,86)(80,84)(83,145)(85,143)(87,141)(89,139)(91,137)(93,135)(95,133)(97,131)(99,129)(101,127)(103,125)(105,123)(107,121)(109,119)(111,117)(113,115)1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 540);