Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #11751487 |
| commutator, cosocle | #91145 | C22 |
| Frattini | C8 | C2×S5 |
| Fitting, hypercenter | C16 | S5 |
| prime radical | #11751494 | C2 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ #91145 ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
148 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 160 |
| transitive degree | μt(G) = 160 |
Permutation generators:
(1,91,41,19,81,87,22,50,39,75,79,40,6,92,65,20,24,90,49,77,14,18,80,64,7,96,73,48,52,89,5,78,35,46,94,72,23,76,70,4,53,71,21,93,42,47,51,69)(2,83,45,30,8,88,33,55,13,86,58,44,11,95,68,31,27,43,63,56,17,29,85,67,12,54,16,62,28,66,10,84,38,60,26,15,34,82,37,9,59,74,32,25,3,61,57,36)(97,140,190,114,134,146,117,184,148,116,112,187,119,132,176,171,113,189,101,170,120,115,164,172,103,111,175,143,109,174,145,162,177,100,141,192,102,163,147,142,99,173,118,139,149,144,133,188)(98,136,154,125,131,180,128,183,104,127,169,150,130,165,153,182,110,152,106,167,155,126,161,191,108,168,122,157,135,151,159,185,124,105,137,179,107,160,181,156,138,121,129,186,123,158,166,178);(1,174,6,189,7,146,23,173)(2,158,24,160,12,126,53,165)(3,180,28,100,17,151,8,116)(4,176,19,190,20,147,48,175)(5,188,21,192,22,172,49,187)(9,159,50,161,31,128,78,166)(10,182,51,183,33,156,80,185)(11,105,52,168,34,127,81,136)(13,121,59,115,38,152,27,144)(14,163,39,140,42,132,35,111)(15,181,56,101,44,153,25,118)(16,191,58,114,45,178,26,143)(18,177,46,120,47,148,75,149)(29,98,76,138,61,108,92,110)(30,106,77,169,62,129,93,137)(32,125,79,186,63,157,94,167)(36,122,84,117,67,154,55,145)(37,150,85,142,68,179,57,171)(40,164,69,141,72,133,64,112)(41,184,70,170,73,162,65,139)(43,104,83,102,74,124,54,119)(60,107,91,135,86,130,96,131)(66,123,95,103,88,155,82,97)(71,99,89,134,90,113,87,109)45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240717);