Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7539 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | D32 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| socle | C2×C17 | #1415 |
| prime radical | C17×#2262 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ C2×C17×C32 ◁ G | |
88 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)(18,19,22,29,26,32,25,57)(20,33,35,76,38,79,58,78)(21,39,42,87,46,90,45,105)(23,49,47,107,53,110,52,113)(24,54,48,75,56,115,51,31)(27,59,60,81,64,118,63,34)(28,65,67,101,69,100,117,43)(30,71,70,97,73,96,109,41)(36,83,82,137,84,138,111,129)(37,85,55,77,86,134,116,135)(40,72,91,131,94,133,106,132)(44,102,98,140,104,144,99,89)(50,66,108,126,112,128,114,127)(61,103,119,142,122,145,121,93)(62,123,120,141,124,80,74,92)(68,95,88,125,130,143,139,136);(18,20)(19,27)(21,40)(22,35)(23,50)(24,55)(25,58)(26,38)(28,66)(29,60)(30,72)(31,74)(32,64)(33,39)(34,43)(36,41)(37,51)(42,91)(44,103)(45,106)(46,94)(47,108)(48,86)(49,61)(52,114)(53,112)(54,62)(56,116)(57,63)(59,65)(67,126)(68,129)(69,128)(70,131)(71,82)(73,133)(75,120)(76,87)(77,102)(78,105)(79,90)(80,136)(81,101)(83,88)(84,97)(85,89)(92,95)(93,99)(96,111)(98,142)(100,118)(104,145)(107,119)(109,132)(110,122)(113,121)(115,124)(117,127)(123,125)(130,137)(134,140)(135,144)(138,139)(141,143)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 527);