Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C22×S5 |
| commutator, cosocle | C2×SL(2,𝔽5) | C23 |
| Fitting, hypercenter | C4⋊C4 | S5 |
| prime radical | C2×#6729 | C22 |
| hypocenter | SL(2,𝔽5) | #41 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
332 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Permutation generators:
(1,5,18)(2,10,24)(3,15,6)(4,20,12)(7,8,23)(9,13,14)(11,19,16)(17,21,22)(25,29,42)(26,34,48)(27,39,30)(28,44,36)(31,32,47)(33,37,38)(35,43,40)(41,45,46)(49,51,50,52)(53,67,70,55,57,58)(54,72,76,56,62,64)(59,68,75,71,60,63)(61,73,66,69,65,74)(77,91,94,79,81,82)(78,96,100,80,86,88)(83,92,99,95,84,87)(85,97,90,93,89,98)(101,104,102,103);(1,44,23,31,24,46,3,34,11,43,12,38)(2,29,9,37,6,32,4,39,17,45,18,40)(5,47,13,48,8,27,15,35,21,36,16,25)(7,42,22,26,10,33,19,30,14,28,20,41)(53,96,75,83,76,98,55,86,63,95,64,90)(54,81,61,89,58,84,56,91,69,97,70,92)(57,99,65,100,60,79,67,87,73,88,68,77)(59,94,74,78,62,85,71,82,66,80,72,93)(101,102)(103,104);(1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,83)(32,84)(33,85)(34,86)(35,87)(36,88)(37,89)(38,90)(39,91)(40,92)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,101,50,102)(51,103,52,104)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240959);