Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C2×C17×#3185 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
1954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 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)(5,8)(6,7)(9,10)(11,12,15,18)(13,19,20,26)(14,23,21,17)(16,24,25,22);(4,7)(8,10)(13,20)(16,25)(19,26)(22,24);(11,13,21,24,15,20,14,22)(12,16,23,26,18,25,17,19);(3,5,6,9)(4,8,7,10)(13,20)(16,25)(19,26)(22,24)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53680);