Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #376×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2397 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D181 |
| commutator, socle, cosocle | C23×C181 | C24 |
| Frattini | C23 | C23×D181 |
| Fitting | #376×C181 | C2 |
| hypercenter | #376 | D181 |
| hypocenter | C181 | #2397 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^180,h^c=h^1803644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 7791);