Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C89 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D89 |
| commutator, hypocenter | C89 | C128 |
| Fitting, cosocle | C64×C89 | C2 |
| socle, prime radical | C2×C89 | C64 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^882944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D89, C2×#26018071, #36442338, … |
| maximal normal subgroup of | C128×D89, C2×#26018071, #36442338, … |
| maximal quotient of | #36440953, C2×#26018071 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2329);