Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#15667725 |
| derived, Sylow | C353 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D353 |
| commutator, hypocenter | C353 | C22×C8 |
| Frattini | C4 | C22×D353 |
| Fitting | C22×C4×C353 | C2 |
| socle, prime radical | C23×C353 | C4 |
| cosocle | C4×C353 | C23 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
2848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36377541, #36377542, #36377549, … |
| maximal normal subgroup of | #36377541, #36377542, #36377549, … |
| maximal quotient of | C2×C4×#15667725, C2×C22⋊#15667725, C2×C4⋊#15667725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 148);