Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of #92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C11 |
No aliases for this group.
| derived, Sylow | C112 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #92150 |
| commutator, hypocenter | C112 | C8 |
| Fitting, socle, prime radical | C2×C112 | C4 |
| cosocle | C11⋊Dic11 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^3,11^2|a^2=b,b^2=c,d^a=d^5e^7,e^a=de^6,d^b=d^10,e^b=e^1068 conjugacy classes — view the full character table.
| maximal subgroup of | #14515509, #14515512, #14515513, … |
| maximal normal subgroup of | #14515509, #14515512, #14515513, … |
| maximal quotient of | #14515452, C2×#11757242 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 16);