Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#19150749 |
| derived, Sylow | C353 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #15667734 |
| commutator, hypocenter | C353 | C2×C16 |
| Frattini | C2 | C2×#15667734 |
| Fitting, socle, prime radical | C22×C353 | C8 |
| cosocle | #15667732 | C22 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C22 | |
28 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19150749, #36378881, C22⋊#19150749, … |
| maximal normal subgroup of | C4×#19150749, #36378881, C22⋊#19150749, … |
| maximal quotient of | C4×#19150749, C22⋊#19150749, C4⋊#19150749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 240);