Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C89 ⋊ #2935 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D89 |
| commutator, socle | C22×C89 | C23×C4 |
| Fitting, prime radical | #532×C89 | C2 |
| cosocle | C2×C4×C89 | C24 |
| hypercenter | #532 | D89 |
| hypocenter | C89 | #2935 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=f,c^2=f,f^2=g,b^a=be,h^a=h^88,d^b=dg,d^c=dg,h^c=h^881282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36448902, #36448906, #36448916, … |
| maximal normal subgroup of | #36448902, #36448906, #36448916, … |
| maximal quotient of | #36526186, #36526196, #36526205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13254);