Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60823 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
2054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27)(28,38)(29,44)(30,36)(31,37)(32,48)(33,42)(34,45)(35,46)(39,54)(40,50)(41,55)(43,51)(47,53)(49,57)(52,56);(18,20,21,25)(19,22,23,24)(26,28)(27,33)(29,40)(30,41)(31,42)(32,43)(34,52)(35,50)(36,51)(37,38)(39,46)(44,54)(45,57)(47,56)(48,55)(49,53);(20,25)(22,24)(26,29)(27,34)(28,39)(30,45)(31,46)(32,47)(33,49)(35,36)(37,53)(38,52)(40,42)(41,56)(43,57)(44,48)(50,55)(51,54);(19,23)(22,24)(26,29)(27,35)(28,40)(30,47)(31,46)(32,45)(33,50)(34,36)(37,44)(38,54)(39,42)(41,56)(43,57)(48,53)(49,55)(51,52);(26,30,31,32)(27,36,37,48)(28,41,42,43)(29,45,46,47)(33,51,38,55)(34,35,53,44)(39,56,40,57)(49,54,52,50)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53811);