Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #556×C167 ⋊ C2 |
| Sylow | C167 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D167 |
| commutator, socle, cosocle | C22×C167 | C25 |
| Fitting | #556×C167 | C2 |
| hypercenter | #556 | D167 |
| hypocenter | C167 | #3480 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10688 |
Polycyclic presentation:
2^7,167|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^166,h^e=h^1662125 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 18102);