Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11604 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #102 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C2×C17 | C2×D4⋊C8 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,29,39,47,25,30,38,27,23,40,21,36)(20,31,34,26,35,43,37,45,32,48,33,42,41,46,49,44);(18,20)(19,26)(21,37)(22,33)(23,41)(24,35)(25,32)(27,43)(28,46)(29,45)(30,42)(31,47)(34,38)(36,48)(39,49)(40,44);(20,32)(26,42)(31,48)(33,34)(35,41)(37,49)(43,46)(44,45)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4592);