Finite Group DatabasebetaFinite Group Databasebeta| order | 150 |
| isoclinism | isoclinic class of #3874 |
| automorphism | Aut(G) = #64480⋊C2 (order 600) · Inn(G) = G · Out(G) = C4 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C52 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C3 | C2 |
| Fitting, socle | C52 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 15 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,7)(2,4,6,13,5,9,12,10,11,14)(3,15);(1,2,4)(3,6,14)(5,10,8)(7,11,13)(9,15,12)Polycyclic presentation:
2,3,5^2|b^a=b^2,d^a=c^4d^4,c^b=cd^3,d^b=c^4d^313 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊C2, C2×#3874, C3×#3874, … |
| maximal normal subgroup of | #3874⋊C2, C2×#3874, C3×#3874, … |
| maximal quotient of | #64470, C2×#3874, #90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(150, 5);