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 ⋊ 2−1+4 |
| Sylow | C5 ⋊ #1010 |
| Sylow | C3 ⋊ #4150 |
| 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 | 2−1+4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ #41 | |
292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,4,5,3)(6,7,8)(9,13,14,12)(10,16,17,21)(11,18,19,20)(15,23,24,22);(9,12,14,13)(10,16,17,21)(11,18,19,20)(15,22,24,23);(9,11,14,19)(10,15,17,24)(12,20,13,18)(16,23,21,22);(2,3)(4,5)(7,8)(9,10)(11,15)(12,16)(13,21)(14,17)(18,22)(19,24)(20,23)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=e,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 | #11749424, #11749425, #11749460, … |
| maximal normal subgroup of | #11749424, #11749425, #11749460, … |
| maximal quotient of | #11756275, #11756277, #11756278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1177);