Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#19150745 |
| derived, Sylow | C353 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #13083443 |
| commutator, hypocenter | C353 | C22×C8 |
| Frattini | C2 | C22×#13083443 |
| Fitting | C2×C4×C353 | C4 |
| socle | C22×C353 | C2×C4 |
| prime radical | C22×D353 | C4 |
| cosocle | Dic353 | C23 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
736 conjugacy classes — view the full character table.
| maximal subgroup of | #36378652, #36378660, #36378662, … |
| maximal normal subgroup of | #36378652, #36378660, #36378662, … |
| maximal quotient of | C2×C4×#15667732, C4×#19150745, #36378755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 229);