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 | D8×A5 |
| commutator | #91145 | C22 |
| Frattini, cosocle | C8 | C22×A5 |
| Fitting, hypercenter | D16 | A5 |
| hypocenter | SL(2,𝔽5) | D8 |
| LCS | G ▷ #91145 ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D16 | |
181 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 192 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 192 points:
(1,103,17,138,34,149,53,109,59,98)(2,177,81,113,8,107,6,119,38,135)(3,110,11,120,24,134,27,108,7,97)(4,116,44,168,62,174,78,132,84,105)(5,118,45,169,63,176,80,133,85,106)(9,189,93,140,25,126,19,144,67,165)(10,190,94,141,26,128,21,145,68,166)(12,148,52,99,28,130,23,102,13,131)(14,155)(15,136,30,146,50,163,55,127,20,100)(16,137,32,147,51,164,57,129,22,101)(18,143,74,186,86,188,92,162,95,125)(29,192,96,170,54,156,46,171,88,185)(31,173,77,111,56,158,48,115,36,160)(33,175,79,112,58,159,49,117,37,161)(35,104)(39,124)(40,180)(41,181)(42,123)(43,167,60,172,76,184,82,157,47,114)(61,187,91,139,83,182,75,142,66,183)(64,121)(65,122)(69,152)(70,154)(71,191)(72,151)(73,153)(87,150)(89,179)(90,178);(1,132,81,174,17,144)(2,180,28,126,14,160)(3,115,7,163,52,146)(4,133,93,176,44,145)(5,162,94,188,45,171)(6,140,24,189,38,100)(8,158,42,165,12,151)(9,181,56,128,40,161)(10,191,58,156,41,183)(11,121,59,127,35,168)(13,116,23,111,53,173)(15,117,20,164,77,147)(16,142,22,184,79,172)(18,113,96,177,74,97)(19,141,50,190,67,101)(21,170,51,192,68,114)(25,159,72,166,31,153)(26,182,73,185,33,178)(27,105,39,136,34,152)(29,104,83,108,71,138)(30,122,84,129,64,169)(32,150,85,157,65,186)(36,118,48,112,78,175)(37,143,49,139,80,187)(43,103,47,99,91,148)(46,134,76,120,88,102)(54,98,90,110,61,124)(55,106,69,137,62,154)(57,125,70,167,63,179)(60,123,95,130,87,135)(66,119,75,109,92,149)(82,107,89,131,86,155)51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240723);