Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2560 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C2×#126×C73 | C2 |
| hypercenter | C2×#126 | D73 |
| hypocenter | C73 | #2560 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
518 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=e,b^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^72,h^c=h^721046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2560×D73, C2×#22615073, #33256163, … |
| maximal normal subgroup of | #2560×D73, C2×#22615073, #33256163, … |
| maximal quotient of | #33008346, #33008617, #33009301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 9652);