Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #919 |
| Sylow | C3 ⋊ #4065 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D15 |
| commutator, cosocle | C3×C4×C5 | C23 |
| Frattini | C4 | C22×D15 |
| Fitting | C3×C5×Q16 | C2 |
| socle | C2×C3×C5 | C2×D4 |
| hypercenter | Q16 | D15 |
| hypocenter | C3×C5 | #135 |
| LCS | G ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
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)(9,11,13,17)(10,15,14,23)(12,21,22,19)(16,24,20,18);(9,10,13,14)(11,18,17,24)(12,20,22,16)(15,21,23,19);(2,3)(4,5)(7,8)(10,14)(11,17)(16,20)(19,21)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=e,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 | #11748293, #11748299, #11748308, … |
| maximal normal subgroup of | #11748293, #11748299, #11748308, … |
| maximal quotient of | #11750889, #11750897, #11750901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 884);