Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #7207 |
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 2 generators on 143 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(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)(80,82,84,94,85,95,100,118,86,96,101,119,102,120,124,138)(81,87,90,105,91,106,113,130,88,92,108,114,109,115,132,136)(83,93,98,116,99,117,123,137,97,103,121,125,122,126,139,140)(89,110,111,133,112,134,135,143,107,104,127,128,131,129,141,142);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,83,89,85,91,99,112,86,88,97,107,102,109,122,131)(82,92,93,110,95,115,117,134,96,87,103,104,120,106,126,129)(84,90,98,111,100,113,123,135,101,108,121,127,124,132,139,141)(94,114,116,133,118,136,137,143,119,105,125,128,138,130,140,142)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=g,e^2=g,g^2=h,b^a=bc,c^a=cf,f^a=fh,d^b=df,i^b=i^78,d^c=dh1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56574);