Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C2×D4×A5 |
| commutator | #6732 | C23 |
| Frattini, cosocle | C4 | C23×A5 |
| Fitting, hypercenter | AGL(1,ℤ/8) | A5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ #6732 ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8) | |
592 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 39 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:
(1,19,24,42,15,5,8,13,30,27)(2,35,40,16,12,9,23,37,6,4)(3,18,33,41,26)(7,34,47,14,20)(10,28,22,48,36)(11,17,44,45,25)(21,32)(29,39)(49,53)(50,87,64,61,90,57,77,54,72,78)(52,60)(55,86,73,81,96)(56,69,75,71,88,67,80,63,83,85)(62,70,89,65,94)(66,91,84,92,95)(74,82,93,76,79);(1,43,23,26,37,3,39,34,16,45,4,46,24,25,42,11,21,33,27,48,5,31,35,36,40,10,29,44,6,47,12,38,13,14,30,20,32,22,15,41)(2,17,8,28,9,7,19,18)(49,81,56,96,69,68,72,55,90,94,60,82,50,93,87,58,71,76,85,91,53,70,67,89,80,59,61,65,78,86,52,92,57,95,77,51,83,66,88,79)(54,74,75,62,64,84,63,73);(1,49,5,53)(2,50,9,57)(3,51,10,58)(4,52,12,60)(6,54,16,64)(7,55,17,65)(8,56,19,67)(11,59,20,68)(13,61,24,72)(14,62,25,73)(15,63,27,75)(18,66,28,76)(21,69,32,80)(22,70,33,81)(23,71,35,83)(26,74,36,84)(29,77,39,87)(30,78,42,90)(31,79,43,91)(34,82,44,92)(37,85,40,88)(38,86,46,94)(41,89,48,96)(45,93,47,95)54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240883);