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, Frattini, cosocle | C8 | C22×A5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Fitting, hypercenter | M32 | A5 |
| socle | C2 | C2×C8×A5 |
| prime radical | C2×#6732 | C4 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C8 ◁ M32 | |
188 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 23 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:
(1,30,22,86,6,31,49,29,7,62,5,60,23,9,21,61)(2,19,33,75,11,20,63,18,12,48,10,46,34,4,32,47)(3,40,45,90,13,64,68,89,17,72,16,71,38,69,37,87)(8,55,58,95,27,56,85,54,28,84,26,82,59,25,57,83)(14,44,73,43,35,67,70,66,42,15,41,74,39,36,65,88)(24,93,80,91,52,50,94,92,53,77,51,96,81,78,79,76)(97,158,118,156,102,105,145,157,103,126,101,182,119,127,117,125)(98,144,129,142,107,100,159,143,108,115,106,171,130,116,128,114)(99,168,141,167,109,165,164,183,113,136,112,186,134,160,133,185)(104,180,154,178,123,121,181,179,124,151,122,191,155,152,153,150)(110,111,169,170,131,132,166,184,138,140,137,139,135,163,161,162)(120,173,176,192,148,174,190,172,149,189,147,187,177,146,175,188);(1,154,39,147,34,101,59,166,52,159,6,181,14,175,2,117,8,137,53,106,7,122,35,176,11,118,27,161,81,128,23,153,42,190,12,145,28,169,24,129)(3,141,13,164,17,112,38,133)(4,179,69,172,62,114,84,185,77,182,19,191,40,187,9,142,25,167,78,125,20,150,64,188,30,143,55,183,93,156,48,178,72,192,31,171,56,186,50,157)(5,155,70,148,63,102,85,110,79,98,21,104,41,149,10,103,26,131,80,107,22,123,65,177,32,119,57,138,94,108,49,124,73,120,33,97,58,135,51,130)(15,170,36,184,44,139,67,162)(16,134,37,99,45,109,68,113)(18,180,89,173,86,115,95,136,91,105,46,121,71,174,29,116,54,160,92,126,47,151,87,189,60,144,82,168,96,127,75,152,90,146,61,100,83,165,76,158)(43,163,66,111,74,132,88,140)96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240691);