Finite Group DatabasebetaFinite Group Databasebeta| order | 11744 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C367 ⋊ C2 |
| Sylow | C367 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D367 |
| commutator, socle, cosocle | C2×C367 | C24 |
| Fitting | #41×C367 | C2 |
| hypercenter | #41 | D367 |
| hypocenter | C367 | H(5,𝔽2) |
| LCS | G ▷ C2×C367 ▷ C367 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,367|b^a=be,d^a=de,c^b=ce,f^c=f^366,f^d=f^3661847 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37554352, #37554355, #37554362, … |
| maximal normal subgroup of | #37554352, #37554355, #37554362, … |
| maximal quotient of | #37554658, #37554660, #37554666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11744, 192);