Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C3×C4 |
| Hall | #14579330 ⋊ C3 |
| Hall | C13×#3861 ⋊ C4 |
| Hall | #3861 ⋊ #261 |
| Sylow | C72 ⋊ C3×#261 |
| Sylow | C13 ⋊ #5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C13 | C3×C4 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,7^2,13|a^2=c,d^a=d^5e^3,e^a=d^3e^2,f^a=f^5,d^b=d^2,e^b=e^2,d^c=d^6,e^c=e^6,f^c=f^1273 conjugacy classes — view the full character table.
| maximal subgroup of | #37524855, #21439678⋊C3, C3×#21439682, … |
| maximal normal subgroup of | #21439678⋊C3, C3×#21439682, C5×#21439682 |
| maximal quotient of | #37524497, C3×#21439682, C3⋊#21439682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 251);