Finite Group DatabasebetaFinite Group Databasebeta| order | 11613 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C79⋊#3862 |
| Fitting, socle, derived, Hall | C72×C79 ⋊ C3 |
| Sylow | C79 ⋊ #3862 |
| Sylow | C72 ⋊ C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C79 | C3 |
| LCS | G ▷ C72×C79 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,79|b^a=b^4,c^a=c^2,d^a=d^231293 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37551149, #37551150, #37551151, … |
| maximal normal subgroup of | #37551149, #37551150, #37551151, … |
| maximal quotient of | C2×C79⋊#3862, C79⋊#89205, C3×C79⋊#3862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11613, 7);