Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C173 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D173 |
| commutator, socle, cosocle | C23×C173 | C23 |
| Fitting, prime radical | C22×D4×C173 | C2 |
| hypercenter | C22×D4 | D173 |
| hypocenter | C173 | #394 |
| LCS | G ▷ C23×C173 ▷ C173 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,173|c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1721742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36352489, #36352491, #36352496, … |
| maximal normal subgroup of | #36352489, #36352491, #36352496, … |
| maximal quotient of | #36351804, #36351806, #36351810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 463);