Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C32 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C16 |
| Frattini, cosocle | C16 | C2×A5 |
| socle | C2 | C16×A5 |
| prime radical | #6732 | C8 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C32 | |
69 conjugacy classes of subgroups.
| minimal degree | μ(G) = 192 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 192 points:
(1,8,2,17,39,7,28,12,3,35)(4,25,9,44,69,20,56,31,15,64)(5,26,10,45,70,22,58,33,16,65)(6,27,11,38,14,23,59,34,13,42)(18,54,29,74,89,47,83,61,43,87)(19,55,30,67,40,48,84,62,36,72)(21,57,32,68,41,49,85,63,37,73)(24,53)(46,82,60,88,71,75,95,86,66,90)(50,78)(51,80)(52,81)(76,92)(77,93)(79,94)(91,96)(97,104,98,113,135,103,124,108,99,131)(100,121,105,140,165,116,152,127,111,160)(101,122,106,141,166,118,154,129,112,161)(102,123,107,134,110,119,155,130,109,138)(114,150,125,170,185,143,179,157,139,183)(115,151,126,163,136,144,180,158,132,168)(117,153,128,164,137,145,181,159,133,169)(120,149)(142,178,156,184,167,171,191,182,162,186)(146,174)(147,176)(148,177)(172,188)(173,189)(175,190)(187,192);(1,150,93,103,58,173,75,122,81,142,56,148,49,121,92,117,28,172,48,104,80,115,82,147,23,191,78,102,57,146,47,181,53,114,55,120,22,180,91,101,27,192,20,155,79,100,54,190,7,179,77,97,26,189,46,154,52,171,25,177,21,152,76,145,8,188,19,124,51,144,95,176,6,178,50,119,85,174,18,153,24,143,84,149,5,151,96,118,59,187,4,123,94,116,83,175)(2,185,44,108,65,111,86,166,17,156,64,99,63,165,66,128,35,184,62,135,37,126,71,164,34,186,36,107,41,163,61,169,13,125,40,134,33,168,43,106,14,170,31,138,16,105,89,141,12,183,15,98,70,140,60,161,3,182,69,113,32,160,88,159,39,162,30,131,68,158,90,133,11,167,67,130,73,132,29,137,38,157,72,109,10,136,74,129,42,139,9,110,45,127,87,112)144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240615);