Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,29)(22,24)(23,28)(25,31)(27,33)(30,32)(34,35)(36,44)(37,40)(38,42)(39,43)(41,45)(46,49)(47,48);(18,20)(19,23)(21,30)(22,27)(24,32)(25,33)(26,29)(28,31)(35,40)(37,38)(41,48)(42,43)(44,49)(45,46);(34,36)(35,41)(37,45)(38,46)(39,47)(40,48)(42,44)(43,49);(19,24)(20,27)(25,29)(28,30)(34,37,39,38)(35,42,43,40)(36,45,47,46)(41,44,49,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11646);