Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ H(5,𝔽2) |
| Sylow | C5 ⋊ #1009 |
| Sylow | C3 ⋊ #4149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D15 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×#41 | C2 |
| hypercenter | #41 | D15 |
| hypocenter | C3×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
332 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 119 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)(10,14,13,16);(10,13)(14,16);(9,10)(11,14)(12,13)(15,16);(2,3)(4,5)(7,8)(11,15)(14,16)Polycyclic presentation:
2^5,3,5|d^2=e,d^a=de,f^a=f^2,g^a=g^4,c^b=ce87 conjugacy classes — view the full character table.
| maximal subgroup of | #11749421, #11749422, #11749467, … |
| maximal normal subgroup of | #11749421, #11749422, #11749467, … |
| maximal quotient of | #11756278, #11756280, #11756282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1176);