Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#117×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Frattini | C22 | C24×D89 |
| Fitting | C2×#117×C89 | C2 |
| hypercenter | C2×#117 | D89 |
| hypocenter | C89 | #3449 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#117 | |
1556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|e^2=f,b^a=bf,c^a=cg,d^a=df,h^a=h^88,c^b=cf,h^c=h^881804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36446263, #36446266, #36461065, … |
| maximal normal subgroup of | #36446263, #36446266, #36461065, … |
| maximal quotient of | #36713000, #36713057, #36713196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17843);