Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×Q8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#41 |
| Sylow | C5 ⋊ D3×#41 |
| Sylow | C3 ⋊ D5×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×Q8 | C22 |
| hypercenter | Q8 | D3×D5 |
| hypocenter | C3×C5 | C2×#41 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2,4,5,3)(6,7,8)(9,11,12,15)(10,13,14,16);(9,10,12,14)(11,16,15,13);(7,8)(11,15)(13,16);(2,3)(4,5)(11,15)(13,16)Polycyclic presentation:
2^5,3,5|c^2=e,d^2=e,d^a=de,g^a=g^4,d^b=de,f^b=f^2,d^c=de60 conjugacy classes — view the full character table.
| maximal subgroup of | #11751959, #11751973, #11754067, … |
| maximal normal subgroup of | #11751959, #11751973, #11754067, … |
| maximal quotient of | #11753329, #11753330, #11753398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1110);