Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C89 ⋊ #2402 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D89 |
| commutator, socle, prime radical, cosocle | C23×C89 | C24 |
| Frattini | C23 | C23×D89 |
| Fitting | #376×C89 | C2 |
| hypercenter | #376 | D89 |
| hypocenter | C89 | #2402 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36457566, #36457567, #36457571, … |
| maximal normal subgroup of | #36457566, #36457567, #36457571, … |
| maximal quotient of | #36476151, #36476172, #36476204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7815);