Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#14583829 |
| derived, Sylow | C173 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10621924 |
| commutator, hypocenter | C173 | C22×C16 |
| Frattini | C4 | C22×#10621924 |
| Fitting | C22×C4×C173 | C4 |
| socle, prime radical | C23×C173 | C8 |
| cosocle | #13063436 | C23 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
752 conjugacy classes — view the full character table.
| maximal subgroup of | #36368601, #36368602, #36368617, … |
| maximal normal subgroup of | #36368601, #36368602, #36368617, … |
| maximal quotient of | C2×C4×#14583829, C2×C22⋊#14583829, C2×C4⋊#14583829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1602);