Finite Group DatabasebetaFinite Group Databasebeta| order | 548 |
| isoclinism | isoclinic class of #10587739 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C137 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C137 | C4 |
| prime radical, cosocle | D137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 137 |
Polycyclic presentation:
2^2,137|a^2=b,c^a=c^100,c^b=c^13638 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10587739, #11764049, C3×#10587739, … |
| maximal normal subgroup of | C2×#10587739, #11764049, C3×#10587739, … |
| maximal quotient of | #11764047, C2×#10587739, C3×#10587739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(548, 3);