Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C353 ⋊ C2 |
| Sylow | C353 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D353 |
| commutator, socle, cosocle | C22×C353 | C23 |
| Fitting | C2×Q8×C353 | C2 |
| prime radical | C2×D1412 | C2 |
| hypercenter | C2×Q8 | D353 |
| hypocenter | C353 | #124 |
| LCS | G ▷ C22×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^352,f^b=f^352,f^c=f^3521774 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36377583, #36377960, #36377962, … |
| maximal normal subgroup of | #36377583, #36377960, #36377962, … |
| maximal quotient of | #36377652, #36377677, #36377688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 135);