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 | C8 | C2×S5 |
| commutator, hypocenter | SL(2,𝔽5) | C2×C8 |
| Fitting, hypercenter | C2×C8 | S5 |
| socle | C2 | C2×A5⋊C8 |
| prime radical | C2×#6732 | C4 |
| cosocle | #91145 | C22 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
184 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 20 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:
(1,137,38,128,27,133,17,127,21,112,14,132,6,122,20,111,11,115,5,109,7,100,3,143)(2,138,35,135,28,140,24,139,34,119,30,129,10,136,18,118,25,144,9,125,46,104,12,141)(4,99,47,97,41,134,32,123,37,113,31,117,16,110,36,102,26,116,15,107,19,101,13,103)(8,108,45,98,42,131,39,124,44,120,43,130,23,126,33,106,40,114,22,121,48,105,29,142)(49,187,59,176,78,157,65,184,51,160,73,185,54,173,75,159,60,175,53,186,62,148,76,170)(50,189,68,183,83,163,72,188,55,167,82,191,58,177,86,166,66,181,57,192,69,152,94,180)(52,172,74,145,91,155,80,174,61,161,88,147,64,169,89,150,77,171,63,156,79,149,90,158)(56,190,84,146,93,164,87,179,67,168,92,151,71,178,95,154,81,182,70,162,85,153,96,165);(1,153,23,189,14,158,16,183,9,178,13,157,5,154,39,192,27,171,32,152,10,179,26,170,6,168,8,177,3,147,4,166,24,190,31,175,17,146,22,188,11,155,15,167,2,162,41,185)(7,145,43,163,18,169,37,160,25,182,45,186,20,149,42,180,34,174,47,176,30,151,48,173,21,150,29,181,35,172,19,148,28,164,33,184,38,161,40,191,46,156,36,159,12,165,44,187)(49,125,67,131,73,115,64,124,86,129,90,134,53,136,84,142,78,132,80,108,55,140,77,103,54,139,85,114,76,133,52,121,68,141,88,116,65,138,95,130,60,143,63,126,69,144,91,117)(50,135,92,123,59,128,71,106,66,122,89,102,57,104,93,99,62,100,87,120,82,127,61,113,58,118,96,107,75,111,56,98,83,137,74,97,72,119,81,110,51,112,70,105,94,109,79,101)72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240683);