Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #394×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #394×C89 | C2 |
| prime radical | #19151506 | C2 |
| hypercenter | #394 | D89 |
| hypocenter | C89 | #2392 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #394 | |
696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^88,h^d=h^881012 conjugacy classes — view the full character table.
| maximal subgroup of | #36464627, #36465116, #36526695, … |
| maximal normal subgroup of | #36464627, #36465116, #36526695, … |
| maximal quotient of | #36476107, #36476122, #36476161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7749);