Finite Group DatabasebetaFinite Group Databasebeta| order | 7124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C137 ⋊ C4 |
| Sylow | C137 ⋊ #261 |
| Sylow | C13 ⋊ Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C137 | C4 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,137|a^2=b,c^a=c^5,d^a=d^136,c^b=c^12551 conjugacy classes — view the full character table.
| maximal subgroup of | #20297119⋊C3, C3×#20297119, C3⋊#20297119, … |
| maximal normal subgroup of | #20297119⋊C3, C3×#20297119, C5×#20297119 |
| maximal quotient of | C3×#20297119, C3⋊#20297119, C5×#20297119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7124, 10);