Finite Group DatabasebetaFinite Group Databasebeta| order | 1156 |
| isoclinism | isoclinic class of #11923883 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C172 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C172 | C4 |
| prime radical, cosocle | C17⋊D17 | C2 |
| LCS | G ▷ C172 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 289 |
Polycyclic presentation:
2^2,17^2|a^2=b,c^a=c^13,d^a=d^13,c^b=c^16,d^b=d^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #11923883⋊C3, C3×#11923883, C3⋊#11923883, … |
| maximal normal subgroup of | #11923883⋊C3, C3×#11923883, C11×#11923883, … |
| maximal quotient of | C3×#11923883, C3⋊#11923883, C11×#11923883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1156, 10);