Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C353 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #13083443 |
| commutator, hypocenter | C353 | C32 |
| Fitting | C8×C353 | C4 |
| socle, prime radical | C2×C353 | C16 |
| cosocle | #19150712 | C2 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^311,f^b=f^352736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26015042, #36378718, #36378719, … |
| maximal normal subgroup of | C2×#26015042, #36378718, #36378719, … |
| maximal quotient of | #36378626, C2×#26015042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 196);