Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #10624761 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #10624761 | C2 |
| Frattini | C33 | C3⋊(C3⋊D3) |
| socle | C3 | #92338 |
| LCS | G ▷ #10624761 | |
| UCS | C1 | |
341 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^3=g^2,b^a=b^2g,c^a=c^2e^2f^2g,d^a=d^2e^2f,e^a=eg^2,g^a=g^2,c^b=ce,d^b=df,e^b=eg,e^c=eg,f^d=fg42 conjugacy classes — view the full character table.
| maximal subgroup of | #72221901, #72221914, #72221932, … |
| maximal normal subgroup of | #72221914, #72221932, #72243781, … |
| maximal quotient of | C2×#13091157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1231);