Finite Group DatabasebetaFinite Group Databasebeta| order | 676 |
| isoclinism | isoclinic class of #10621721 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C169 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C169 | C4 |
| Frattini, socle | C13 | #261 |
| prime radical, cosocle | D169 | C2 |
| LCS | G ▷ C169 | |
| UCS | C1 | |
9 conjugacy classes of subgroups.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 169 |
Polycyclic presentation:
2^2,13^2|a^2=b,c^13=d,c^a=c^8d^7,d^a=d^8,c^b=c^12d^12,d^b=d^1246 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10621721, #10621721⋊C3, C3×#10621721, … |
| maximal normal subgroup of | C2×#10621721, #10621721⋊C3, C3×#10621721, … |
| maximal quotient of | #13062557, C2×#10621721, C3×#10621721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(676, 3);