Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | #6879 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | #4185 |
| commutator, Fitting, cosocle, hypocenter | #6879 | C2 |
| Frattini | C3×C9 | C3⋊D3 |
| LCS | G ▷ #6879 | |
| UCS | C1 ◁ C3 | |
45 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 3 generators on 27 points:
(2,7)(3,11)(9,20)(10,15)(13,23)(14,24)(18,26)(19,22)(25,27);(1,3,11)(2,8,7)(4,15,10)(5,19,22)(6,13,23)(9,21,20)(12,24,14)(16,27,25)(17,26,18);(1,2,7)(3,12,11)(4,14,24)(5,18,26)(6,10,15)(8,9,20)(13,16,23)(17,25,27)(19,21,22)Polycyclic presentation:
2,3^5|d^3=f^2,b^a=b^2,c^a=c^2,e^a=e^2f,c^b=cd,d^b=de,e^b=ef,d^c=de^2f,e^c=ef^231 conjugacy classes — view the full character table.
| maximal subgroup of | #92191⋊C2, C2×#92216, #13090585, … |
| maximal normal subgroup of | #92191⋊C2, C2×#92216, #13090585, … |
| maximal quotient of | #11757339, C2×#92216, #13090511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 61);