Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C17 · Schur multiplier (H2) = C220 |
| direct product | C17×#63103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C26 |
| commutator, Frattini, cosocle | C2 | C27×C17 |
| socle | C2×C17 | C27 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ G | |
59452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 7 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,25)(22,27)(23,26)(24,30)(29,40)(31,41)(32,37)(33,38)(34,39)(35,42)(36,44)(43,48)(45,47)(46,49);(18,20)(19,24)(21,29)(22,31)(23,30)(25,35)(26,28)(27,36)(32,42)(33,43)(34,44)(37,40)(38,46)(39,41)(45,49)(47,48);(18,21)(19,25)(20,29)(22,33)(23,32)(24,35)(26,37)(27,38)(28,40)(30,42)(31,43)(34,45)(36,46)(39,47)(41,48)(44,49);(21,32)(25,37)(29,42)(33,45)(35,40)(38,47)(43,49)(46,48);(20,30)(24,28)(29,42)(31,44)(35,40)(36,41)(43,49)(46,48);(19,26)(24,28)(25,37)(27,39)(35,40)(36,41)(38,47)(46,48);(18,22,23,34)(19,27,26,39)(20,31,30,44)(21,33,32,45)(24,36,28,41)(25,38,37,47)(29,43,42,49)(35,46,40,48)2210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 56091);