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×#62861 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6854 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)(18,19,21,23)(20,22,24,25)(26,27)(28,33)(29,39)(30,34)(31,45)(32,36)(35,46)(37,47)(38,41)(40,42)(43,55)(44,50)(48,52)(49,56)(51,53)(54,57);(18,19)(20,22)(21,23)(24,25)(26,28,32,39)(27,33,36,29)(30,42,44,37)(31,38,46,52)(34,40,50,47)(35,48,45,41)(43,54,56,51)(49,53,55,57);(26,29)(27,28)(30,40)(31,41)(32,33)(34,37)(35,38)(36,39)(42,50)(43,53)(44,47)(45,52)(46,48)(49,51)(54,55)(56,57);(26,27)(28,33)(29,39)(30,34)(31,35)(32,36)(37,47)(38,48)(40,42)(41,52)(43,49)(44,50)(45,46)(51,57)(53,54)(55,56);(26,30,32,44)(27,34,36,50)(28,37,39,42)(29,40,33,47)(31,43,46,56)(35,49,45,55)(38,51,52,54)(41,53,48,57);(18,20,21,24)(19,22,23,25)(26,31)(27,35)(28,38)(29,41)(30,43)(32,46)(33,48)(34,49)(36,45)(37,51)(39,52)(40,53)(42,54)(44,56)(47,57)(50,55)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55849);