Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61021 |
| 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 | |
1724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 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)(21,25)(22,24)(23,27)(28,32)(29,31)(30,33)(34,35)(36,40)(37,42)(38,41)(39,43)(44,47)(45,48)(46,49);(18,20)(19,23)(21,28)(22,27)(24,26)(25,30)(29,33)(31,32)(34,36,39,38)(35,40,43,41)(37,45,46,44)(42,48,49,47);(20,27)(23,26)(28,33)(30,32)(35,41)(36,38)(40,43)(42,48)(44,45)(47,49);(19,24)(23,26)(25,31)(30,32)(34,37,39,46)(35,42,43,49)(36,44,38,45)(40,47,41,48);(18,21,22,29)(19,25,24,31)(20,28,27,33)(23,30,26,32)(37,46)(42,49)(44,45)(47,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54009);