Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C373 ⋊ C2 |
| Sylow | C373 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D373 |
| commutator, socle, cosocle | C22×C373 | C23 |
| Fitting | C2×D4×C373 | C2 |
| hypercenter | C2×D4 | D373 |
| hypocenter | C373 | #121 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,373|b^2=d,b^a=bd,c^a=ce,f^c=f^3721874 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37559554, #37559559, #37559564, … |
| maximal normal subgroup of | #37559554, #37559559, #37559564, … |
| maximal quotient of | #37559279, #37559298, #37559310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 117);