Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #396×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2842 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #396×C89 | C2 |
| prime radical | C24×D89 | C22 |
| hypercenter | #396 | D89 |
| hypocenter | C89 | #2842 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #396 | |
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|b^2=eg,c^2=g,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^d=h^88994 conjugacy classes — view the full character table.
| maximal subgroup of | #2842×D89, C2×#26028515, #36760852, … |
| maximal normal subgroup of | #2842×D89, C2×#26028515, #36760852, … |
| maximal quotient of | #36485220, #36485222, #36485228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12773);