Finite Group DatabasebetaFinite Group Databasebeta| order | 11488 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C359 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D359 |
| commutator, socle, cosocle | C22×C359 | C23 |
| Fitting, prime radical | C2×D4×C359 | C2 |
| hypercenter | C2×D4 | D359 |
| hypocenter | C359 | #124 |
| LCS | G ▷ C22×C359 ▷ C359 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,359|b^2=e,c^2=d,b^a=bd,c^a=ce,f^b=f^358,f^c=f^3581804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37526237, #37526614, #37526621, … |
| maximal normal subgroup of | #37526237, #37526614, #37526621, … |
| maximal quotient of | #37526308, #37526337, #37526346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11488, 133);