Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C353 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#15667734 |
| commutator, socle | C2×C353 | C2×C8 |
| Fitting, prime radical | C22×C353 | C8 |
| cosocle | #15667732 | C22 |
| hypercenter | C22 | #15667734 |
| hypocenter | C353 | M32 |
| LCS | G ▷ C2×C353 ▷ C353 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^283,f^c=f^311,f^d=f^352196 conjugacy classes — view the full character table.
| maximal subgroup of | #36378885, #36378886, C2×#26015088, … |
| maximal normal subgroup of | #36378885, #36378886, C2×#26015088, … |
| maximal quotient of | #36378881, C22⋊#19150749, #36378890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 242);