Finite Group DatabasebetaFinite Group Databasebeta| order | 968 |
| isoclinism | isoclinic class of #11757261 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C112 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112 | C8 |
| prime radical | C11⋊D11 | C4 |
| cosocle | #92150 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
14 conjugacy classes of subgroups.
| transitive degree | μt(G) = 44 |
Polycyclic presentation:
2^3,11^2|a^2=b,b^2=c,d^a=d^9e^3,e^a=de^10,d^b=d^7e^2,e^b=d^8e^4,d^c=d^10,e^c=e^1023 conjugacy classes — view the full character table.
| maximal subgroup of | #11757261⋊C2, C2×#11757261, #72214718, … |
| maximal normal subgroup of | #11757261⋊C2, C2×#11757261, #72214718, … |
| maximal quotient of | #14515509, C2×#11757261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(968, 35);