Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | #577×C71 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C24×C71 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ #41×C71 ◁ G | |
258 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 1136 |
A minimal faithful permutation representation — 4 generators on 87 points:
(1,2,5,9)(3,7,10,14)(4,6,12,8)(11,13,16,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(2,6)(4,12)(7,13)(8,9)(11,16)(14,15);(1,3)(2,7)(4,11)(5,10)(6,13)(8,15)(9,14)(12,16);(3,10)(7,14)(11,16)(13,15)1562 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C71×#3288, C71×#3289, C71×#3290, … |
| maximal normal subgroup of | C71×#3288, C71×#3289, C71×#3290, … |
| maximal quotient of | C71×#2897, C71×#2898, C71×#2912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 258);