Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| prime radical | C17×#3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(27,28)(31,44)(33,36)(34,37)(40,53)(42,54)(45,48)(51,57);(18,19)(20,23)(21,22)(24,25)(26,27,32,28)(29,33,41,36)(30,37,43,34)(31,35,44,38)(39,48,52,45)(40,46,53,49)(42,50,54,47)(51,56,57,55);(18,20,21,24)(19,23,22,25)(26,28,32,27)(29,33,41,36)(30,37,43,34)(31,38,44,35)(39,45,52,48)(40,46,53,49)(42,50,54,47)(51,55,57,56);(26,29)(27,33)(28,36)(30,39)(31,40)(32,41)(34,45)(35,46)(37,48)(38,49)(42,51)(43,52)(44,53)(47,55)(50,56)(54,57);(26,30,32,43)(27,34,28,37)(29,39,41,52)(31,42,44,54)(33,45,36,48)(35,47,38,50)(40,51,53,57)(46,55,49,56);(26,31)(27,35)(28,38)(29,40)(30,42)(32,44)(33,46)(34,47)(36,49)(37,50)(39,51)(41,53)(43,54)(45,55)(48,56)(52,57)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55848);