Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of #10625285 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | H(3,𝔽5)⋊C3 ⋊ C4 |
| Sylow | H(3,𝔽5) ⋊ Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10625285 |
| commutator, hypocenter | H(3,𝔽5)⋊C3 | C4 |
| Frattini, socle | C2×C5 | #3874 |
| Fitting | C2×H(3,𝔽5) | D3 |
| prime radical, cosocle | C2×H(3,𝔽5)⋊C3 | C2 |
| LCS | G ▷ H(3,𝔽5)⋊C3 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 300 |
Polycyclic presentation:
2^2,3,5^3|a^2=b,c^a=c^2,d^a=d^2e^4f^2,e^a=d^3e^3,f^a=f^4,d^c=d^2e^4,e^c=d^2e^2f^4,e^d=ef38 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 13);