Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #401×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2801 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #401×C89 | C2 |
| prime radical | C22×D356 | C22 |
| hypercenter | #401 | D89 |
| hypocenter | C89 | #2801 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #401 | |
420 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=efg,b^2=e,c^2=eg,d^2=f,b^a=be,c^a=cf,d^a=def,h^a=h^88,c^b=cg,d^b=de,h^b=h^88,h^d=h^881000 conjugacy classes — view the full character table.
| maximal subgroup of | #36762454, #36762461, #36762535, … |
| maximal normal subgroup of | #36762454, #36762461, #36762535, … |
| maximal quotient of | #36482774, #36483047, #36483578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 12420);