Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#15667734 |
| unambiguous semidirect product | #13083443⋊C8 |
| Fitting | C4×C353 ⋊ C8 |
| derived, Sylow | C353 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #15667734 |
| commutator, hypocenter | C353 | C4×C8 |
| Frattini | C2 | C2×#15667734 |
| Fitting | C4×C353 | C8 |
| socle | C2×C353 | C2×C8 |
| prime radical | C2×D353 | C2×C4 |
| cosocle | C2×#13083443 | C22 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#15667734, #36378871, D4⋊#15667734, … |
| maximal normal subgroup of | C8×#15667734, #36378871, D4⋊#15667734, … |
| maximal quotient of | C8×#15667734, #36378871, (C2×#15667734)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 237);