Finite Group DatabasebetaFinite Group Databasebeta| order | 240 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | Aut(G) = C2×S5 (order 240) · Inn(G) = A5 · Out(G) = C22 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | SL(2,𝔽5) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C2 |
| Frattini, socle, cosocle | C2 | C2×A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,20,17,5,12)(2,3,9,19,10)(4,14,22,11,6)(7,8,15,13,16);(2,18)(5,11)(6,21)(7,24)(9,17)(10,16)(12,23)(13,20)(14,19)(15,22)18 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(240, 93);