Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, Hall | C5×C132 ⋊ Dic7 |
| derived, Hall | C5×C132⋊C7 ⋊ C4 |
| Hall | C132⋊C7 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C7⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #17990053 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C132⋊C7 | C4 |
| Fitting, socle | C5×C132 | Dic7 |
| prime radical, cosocle | C5⋊((C13⋊D13)⋊C7) | C2 |
| LCS | G ▷ C5×C132⋊C7 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 455 |
Polycyclic presentation:
2^2,5,7,13^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^7f^9,f^a=e^6f^6,c^b=c^4,e^b=e^12,f^b=f^12,e^d=e^9f^5,f^d=e^4f^1147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 58);