Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #534×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #15667981 |
| commutator, cosocle | C24×C89 | C23 |
| Frattini | C24 | C22×D89 |
| Fitting | #534×C89 | C2 |
| socle | C22×C89 | #120 |
| hypercenter | #534 | D89 |
| hypocenter | C89 | #2021 |
| LCS | G ▷ C24×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #534 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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^a=bd,c^a=ce,f^a=fg,c^b=cf,h^b=h^88,d^c=dg994 conjugacy classes — view the full character table.
| maximal subgroup of | #36466455, #36466460, #36466472, … |
| maximal normal subgroup of | #36466455, #36466460, #36466472, … |
| maximal quotient of | #36454622, #36454629, #36454636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 5634);