Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic173 |
| derived, Sylow | C173 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D173 |
| commutator, hypocenter | C173 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D173 |
| Fitting | C22×C8×C173 | C2 |
| socle, prime radical | C23×C173 | C2×C4 |
| cosocle | C2×C4×C173 | C23 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
2816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36351640, #36351644, C4×C8×Dic173, … |
| maximal normal subgroup of | #36351640, #36351644, C4×C8×Dic173, … |
| maximal quotient of | C2×C8×#13063436, C2×#26011213, C8×#14583810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 494);