Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #13570 |
482 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,4,6,20)(2,8,12,11)(3,14,17,18)(5,19,23,22)(7,24,26,25)(9,10,27,30)(13,29,28,32)(15,31,21,16)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3)(2,7)(4,18)(5,21)(6,17)(8,25)(9,28)(10,29)(11,24)(12,26)(13,27)(14,20)(15,23)(16,22)(19,31)(30,32);(1,2,5,10)(3,13,16,7)(4,8,19,27)(6,12,23,30)(9,20,11,22)(14,29,15,24)(17,28,31,26)(18,32,21,25)(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)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=h,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^78,c^b=ch,d^b=dh,e^b=ef,f^b=fh,g^b=gh,e^d=egh,f^d=fh,f^e=fh1276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89827);