Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C373 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D373 |
| commutator, socle | C2×C373 | C22×C4 |
| Fitting, prime radical | #41×C373 | C2 |
| cosocle | C4×C373 | C23 |
| hypercenter | #41 | D373 |
| hypocenter | C373 | #131 |
| LCS | G ▷ C2×C373 ▷ C373 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,373|a^2=d,d^2=e,f^a=f^372,c^b=ce1880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37559536, #37559539, #37559541, … |
| maximal normal subgroup of | #37559536, #37559539, #37559541, … |
| maximal quotient of | #37559378, #37559389, #37559449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 153);