Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60828 |
| 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 | |
2018 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)(28,36)(29,40)(30,32)(31,44)(33,39)(34,41)(35,43)(37,51)(38,49)(42,48)(45,46)(47,57)(50,52)(53,54)(55,56);(18,20,21,25)(19,22,23,24)(27,32)(33,46)(34,40)(35,44)(36,49)(47,54)(48,55)(50,51);(20,25)(22,24)(26,28,30,38)(27,33,32,46)(29,37,41,52)(31,45,43,39)(34,47,40,54)(35,49,44,36)(42,57,56,53)(48,51,55,50);(19,23)(22,24)(26,29)(27,34)(28,37)(30,41)(31,42)(32,40)(33,47)(35,48)(36,50)(38,52)(39,53)(43,56)(44,55)(45,57)(46,54)(49,51);(29,41)(34,40)(37,52)(42,56)(47,54)(48,55)(50,51)(53,57)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53816);