Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#8234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C2×C17×#127 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C43×C17 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,27)(24,25)(28,29)(30,31,34,37)(32,36,33,35);(22,23,25,28,26,29,24,27)(31,35)(32,33)(36,37);(18,20,21,19)(30,32,34,33)(31,36,37,35)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1222);