Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C17×#3212 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
2218 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)(5,9)(6,8)(7,10)(11,12)(13,21)(14,20)(15,17)(16,19)(18,23)(22,26)(24,25);(3,5,6,10)(4,7,8,9)(12,17)(13,22)(19,20)(23,24);(5,10)(7,9)(11,13)(12,18)(14,23)(15,22)(16,24)(17,25)(19,21)(20,26);(4,8)(7,9)(11,14,15,16)(12,19,17,20)(13,23,22,24)(18,21,25,26)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53769);