Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3061 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23)(24,34)(25,30)(26,29)(27,32)(28,36)(31,41)(33,40)(35,43)(37,51)(38,47)(39,45)(42,52)(44,50)(46,53)(48,49);(18,19)(20,21)(22,24)(23,28)(25,36)(26,37)(27,35)(29,44)(30,34)(31,42)(32,47)(33,43)(38,40)(39,50)(41,49)(45,51)(46,48)(52,53);(18,20,21,19)(23,29)(24,35)(26,41)(27,40)(28,42)(30,45)(31,33)(32,46)(34,48)(36,38)(37,50)(39,53)(43,51)(44,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6373);