Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #10597183 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Hall | C3×C52 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic3 |
| Sylow | C3 ⋊ #87830 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10597183 |
| commutator, hypocenter | C3×C52 | C42 |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical, cosocle | C2×C3×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=c,e^a=e^2,f^a=f^4,f^b=f^3,g^b=g^2,f^c=f^4,g^c=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87830, #72224581, #72224584, … |
| maximal normal subgroup of | D3×#87830, #72224581, #72224584, … |
| maximal quotient of | #72224596, #72229331, C2×#11925359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 569);