Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | #525×C71 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C71 |
| socle | C22×C71 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ G | |
330 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1136 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2)(3,4)(5,6)(7,10)(8,9)(11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(6,9)(10,12);(2,4);(5,7,8,11)(6,10,9,12)1988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C71×#1501, C71×#1504, C71×#1513, … |
| maximal normal subgroup of | C71×#1501, C71×#1504, C71×#1513, … |
| maximal quotient of | C71×#2280, C71×#2290, C71×#2296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 206);