Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C17 · Schur multiplier (H2) = C220 |
| direct product | C24×#41×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4×C17 | C22 |
| commutator, Frattini, cosocle | C2 | C27×C17 |
| socle | C25×C17 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4×C17 ◁ G | |
65470 conjugacy classes of subgroups; only the 59038 normal subgroups are shown.
This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 59038 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 7 generators on 33 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6);(7,8);(9,10)(11,14)(12,13)(15,16);(10,13)(14,16);(9,11,12,15)(10,14,13,16)2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 56085);