Finite Group DatabasebetaFinite Group Databasebeta| order | 1156 |
| isoclinism | isoclinic class of #11923876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C289 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C289 | C4 |
| Frattini, socle | C17 | #595 |
| prime radical, cosocle | D289 | C2 |
| LCS | G ▷ C289 | |
| UCS | C1 | |
9 conjugacy classes of subgroups.
| minimal degree | μ(G) = 289 |
| transitive degree | μt(G) = 289 |
Polycyclic presentation:
2^2,17^2|a^2=b,c^17=d^11,c^a=c^13d,d^a=d^13,c^b=c^16d^6,d^b=d^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11923876, C3⋊#11923876, C11×#11923876, … |
| maximal normal subgroup of | C3×#11923876, C11×#11923876, C13×#11923876, … |
| maximal quotient of | C3×#11923876, C3⋊#11923876, C11×#11923876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1156, 3);