Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #2377 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator | C22×C89 | C23×C4 |
| Fitting, prime radical | C2×#121×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| hypercenter | C2×#121 | D89 |
| hypocenter | C89 | #2377 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
576 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 213 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,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^88,c^b=cef,d^b=de1270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36451447, #36451451, #36451461, … |
| maximal normal subgroup of | #36451447, #36451451, #36451461, … |
| maximal quotient of | #36476049, #36476063, #36476067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 7667);