Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C2×C17×#1291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C24×C17 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4)(5,7)(6,9)(8,10)(11,12,14,19,16,18,15,20)(13,21,22,26,23,17,24,25);(4,7,9,8)(11,13,15,22,16,23,14,24)(12,17,20,25,18,21,19,26)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 979);