Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C173 ⋊ C2 |
| Sylow | C173 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D173 |
| commutator, socle | C2×C173 | C22×C8 |
| Fitting | M32×C173 | C2 |
| prime radical | #14583826 | C4 |
| cosocle | C8×C173 | C23 |
| hypercenter | M32 | D173 |
| hypocenter | C173 | #504 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|a^2=d,d^2=e,e^2=f,g^a=g^172,c^b=cf,g^c=g^1721760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36355397, #36355399, #36355402, … |
| maximal normal subgroup of | #36355397, #36355399, #36355402, … |
| maximal quotient of | #36355161, #36355162, #36355175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 967);