Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C16 | S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Frattini | C8 | C2×S5 |
| socle | C2 | C8×S5 |
| prime radical | #91870 | C4 |
| cosocle | #91145 | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C16 | |
155 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Permutation generators:
(1,83,26,56,5,94,31,70,6,66,41,71,17,82,13,87)(2,86,23,84,9,55,39,85,10,68,8,95,24,69,22,67)(3,72,32,92,11,50,4,93,14,57,15,96,27,58,16,81)(7,51,19,61,20,59,36,74,21,62,37,79,38,75,47,89)(12,53,45,88,25,54,48,91,30,65,33,90,28,49,44,77)(18,76,43,80,34,60,42,52,35,73,29,63,46,78,40,64)(97,179,122,152,101,190,127,166,102,162,137,167,113,178,109,183)(98,182,119,180,105,151,135,181,106,164,104,191,120,165,118,163)(99,168,128,188,107,146,100,189,110,153,111,192,123,154,112,177)(103,147,115,157,116,155,132,170,117,158,133,175,134,171,143,185)(108,149,141,184,121,150,144,187,126,161,129,186,124,145,140,173)(114,172,139,176,130,156,138,148,131,169,125,159,142,174,136,160);(1,118,31,102,10,109,16,98,11,100,8,123,5,119,41,113,24,122,32,105,14,111,22,99,6,135,13,97,2,127,4,106,27,112,23,107,17,104,26,101,9,137,15,120,3,128,39,110)(7,136,33,117,30,141,37,108,46,115,29,130,20,139,44,134,28,144,47,121,18,132,40,131,21,138,45,103,12,129,19,126,34,133,43,142,38,125,48,116,25,140,36,124,35,143,42,114)(49,191,88,150,55,186,64,165,60,148,85,174,53,163,91,161,68,173,80,182,73,159,95,172,54,180,90,145,69,184,52,151,78,160,67,156,65,181,77,149,86,187,63,164,76,176,84,169)(50,177,74,154,82,185,71,190,51,152,96,158,57,188,79,168,83,157,87,162,59,166,81,171,58,189,89,146,94,170,56,178,62,167,92,147,72,192,61,153,66,175,70,179,75,183,93,155)96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240684);