Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = D4×S5 (order 960) · Inn(G) = C2×S5 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2 | C2×S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C22 |
| Fitting, hypercenter | C4 | S5 |
| prime radical | #6732 | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2 ◁ C4 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,3,5,15,8,2,7,10)(4,6,12,18,14,9,13,21)(11,24,20,29,16,19,22,30)(17,31,26,34,23,25,27,35)(28,40,42,48,32,36,44,47)(33,43,45,38,39,41,46,37);(1,22,12,3,26,21,8,20,13,2,27,18)(4,16,7,6,23,15,14,11,5,9,17,10)(19,28,45,35,40,43,24,32,46,34,36,41)(25,33,44,29,38,48,31,39,42,30,37,47)18 conjugacy classes — view the full character table.
| maximal subgroup of | #11751493, #11751495, #11751520, … |
| maximal normal subgroup of | #11751493, #11751495, #11751520, … |
| maximal quotient of | C4⋊#6728, #11751505, #11751510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 947);