Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #912 |
| Sylow | C3 ⋊ #4058 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D15 |
| commutator, cosocle | C3×C4×C5 | C23 |
| Frattini | C4 | C22×D15 |
| Fitting | C3×C5×D8 | C2 |
| socle | C2×C3×C5 | C2×D4 |
| hypercenter | D8 | D15 |
| hypocenter | C3×C5 | #135 |
| LCS | G ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,7,8)(10,15)(11,18)(12,21)(14,22)(17,24)(19,20);(9,11)(10,14)(12,18)(13,20)(15,17)(16,24)(19,21)(22,23);(2,3)(4,5)(7,8)(9,10)(11,17)(12,16)(13,15)(14,20)(18,22)(19,24)(21,23)Polycyclic presentation:
2^5,3,5|d^2=e,b^a=be,c^a=ce,f^a=f^2,g^a=g^4,c^b=cd,d^b=de,d^c=de63 conjugacy classes — view the full character table.
| maximal subgroup of | #11748269, #11748275, #11748284, … |
| maximal normal subgroup of | #11748269, #11748275, #11748284, … |
| maximal quotient of | #11750859, #11750867, #11750868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 877);