Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of C5⋊#226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#41 ⋊ D3 |
| Sylow | C5 ⋊ #985 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C5⋊S4 |
| commutator, cosocle, hypocenter | C5×SL(2,𝔽3) | C22 |
| Frattini | C2 | C2×C5⋊S4 |
| Fitting | C5×#41 | D3 |
| socle | C2×C5 | C2×S4 |
| LCS | G ▷ C5×SL(2,𝔽3) | |
| UCS | C1 ◁ C4 | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,6,12,8,3,14,5,15,10,2,11,16)(4,7,9,13)(17,18,20,21,19);(3,4)(6,7)(9,11)(10,12)(13,15)(14,16)(18,19)(20,21)Polycyclic presentation:
2^2,3,5,2^3|b^2=g,e^2=g,f^2=g,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^c=fg,f^c=ef,f^e=fg44 conjugacy classes — view the full character table.
| maximal subgroup of | #11751616, #11751618, #11752123, … |
| maximal normal subgroup of | #11751616, #11751618, #11752123, … |
| maximal quotient of | C4×C5⋊#226, #11752108, C4×C5⋊GL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1031);