Finite Group DatabasebetaFinite Group Databasebeta| order | 148 |
| isoclinism | isoclinic class of #3866 |
| automorphism | Aut(G) = AGL(1,𝔽37) (order 1332) · Inn(G) = G · Out(G) = C9 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C37 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37 | C4 |
| prime radical, cosocle | D37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 37 |
A minimal faithful permutation representation — 2 generators on 37 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,26)(14,21,19,22)(16,23,24,20)(25,30,31,29)(27,32,33,28)(34,36,37,35);(1,2,5,10,19,13,6,11,20,28,31,24,15,22,29,35,37,33,26,17,27,34,36,30,21,8,16,25,32,23,12,3,7,14,18,9,4)Polycyclic presentation:
2^2,37|a^2=b,c^a=c^31,c^b=c^3613 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#3866, #3866⋊C3, C3×#3866, … |
| maximal normal subgroup of | C2×#3866, #3866⋊C3, C3×#3866, … |
| maximal quotient of | #64438, C2×#3866, C3×#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(148, 3);