Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C17 · Schur multiplier (H2) = C214 |
| direct product | C17×#62653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator | C2 | C25×C4×C17 |
| Frattini, cosocle | C22 | C26×C17 |
| prime radical | C22×C17×2−1+4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
10930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,29)(25,30)(26,38)(27,28)(31,39)(32,42)(33,47)(34,40)(35,44)(36,50)(37,41)(43,48)(45,51)(46,53)(49,52);(23,28)(29,40)(30,41)(31,38)(42,44)(43,47)(45,50)(52,53);(22,24,27,34)(23,29,28,40)(25,35,37,32)(26,33,39,48)(30,44,41,42)(31,43,38,47)(36,49,51,46)(45,53,50,52);(22,25,27,37)(23,30,28,41)(24,32,34,35)(26,36,39,51)(29,42,40,44)(31,45,38,50)(33,46,48,49)(43,52,47,53);(22,23)(24,29)(25,30)(26,31)(27,28)(32,42)(33,43)(34,40)(35,44)(36,45)(37,41)(38,39)(46,52)(47,48)(49,53)(50,51);(22,26)(23,31)(24,33)(25,36)(27,39)(28,38)(29,43)(30,45)(32,46)(34,48)(35,49)(37,51)(40,47)(41,50)(42,52)(44,53)2210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55641);