Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C71 · Schur multiplier (H2) = C22 |
| direct product | #464×C71 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C71 |
| prime radical | C2×D4×C71 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C42×C71 ◁ G | |
112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 3 generators on 91 points:
(2,4)(5,6)(7,13)(8,10)(9,17)(11,15)(12,16)(14,20)(18,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2,3,4)(6,10)(11,19)(12,17)(13,20);(5,7,8,14)(6,11,10,19)(9,18,16,15)(12,20,17,13)1349 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#464×C71, C71×#3035, C71×#3037, … |
| maximal normal subgroup of | C2×#464×C71, C71×#3035, C71×#3037, … |
| maximal quotient of | C71×#1678, C71×#1680, C71×#1682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 145);