Finite Group DatabasebetaFinite Group Databasebeta| order | 11632 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C727 ⋊ C2 |
| Sylow | C727 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D727 |
| commutator, socle, cosocle | C2×C727 | C23 |
| Fitting | Q8×C727 | C2 |
| hypercenter | Q8 | D727 |
| hypocenter | C727 | #41 |
| LCS | G ▷ C2×C727 ▷ C727 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,727|c^2=d,b^a=bd,e^a=e^726,e^b=e^726,e^c=e^7261825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37551569, #37551571, #37551575, … |
| maximal normal subgroup of | #37551569, #37551571, #37551575, … |
| maximal quotient of | #37551506, #37551510, Q8×Dic727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11632, 41);