Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C181 ⋊ #2351 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D181 |
| commutator | C22×C181 | C23×C4 |
| Fitting | #389×C181 | C2 |
| socle, prime radical, cosocle | C23×C181 | C24 |
| hypercenter | #389 | D181 |
| hypocenter | C181 | #2351 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #389 | |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
Polycyclic presentation:
2^7,181|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^180,h^d=h^1802570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 7429);