Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #14515301 |
| automorphism | Aut(G) = #72240859 (order 7680) · Inn(G) = #11757162 · Out(G) = D4 |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C42 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C25 | A5 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
121 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,7,12,15,9)(3,8,13,6,5)(10,16,17,21,20)(11,18,22,19,14);(1,14,18)(2,11,7)(3,5,16)(4,10,17)(6,23,8)(9,24,12)(13,19,22)(15,20,21)16 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240999);