Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C353 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #13083443 |
| commutator, hypocenter | C353 | C2×C16 |
| Frattini | C4 | C2×#13083443 |
| Fitting | C8×C353 | C4 |
| socle | C2×C353 | C2×C8 |
| prime radical | C2×D353 | C8 |
| cosocle | #15667725 | C22 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=c,c^2=d,d^2=e,f^a=f^311,f^b=f^352,f^c=f^352736 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#13083443, #36378674, #36378699, … |
| maximal normal subgroup of | C16×#13083443, #36378674, #36378699, … |
| maximal quotient of | #36378673, #36378682, #36378708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 219);