Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, Hall | C72×C13 ⋊ Dic3 |
| derived, Hall | C13×#3862 ⋊ C4 |
| Hall | #3862 ⋊ #261 |
| Sylow | C72 ⋊ C3⋊#261 |
| Sylow | C13 ⋊ #10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C13×#3862 | C4 |
| Fitting, socle | C72×C13 | Dic3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,7^2|a^2=b,c^a=c^2,d^a=d^5,e^a=e^3f^4,f^a=ef^4,d^b=d^12,e^b=e^6,f^b=f^6,e^c=e^2f^6,f^c=f^467 conjugacy classes — view the full character table.
| maximal subgroup of | #37524851, #37524852, #37524855, … |
| maximal normal subgroup of | #37524851, #37524852, #37524855, … |
| maximal quotient of | #37524490, C3×#21439675, C3⋊#21439675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 244);