Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C173 ⋊ C2 |
| Sylow | C173 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D173 |
| commutator, socle, cosocle | C2×C173 | C25 |
| Fitting | H(5,𝔽2)×C173 | C2 |
| hypercenter | H(5,𝔽2) | D173 |
| hypocenter | C173 | #585 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
810 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|e^2=f,b^a=bf,d^a=df,c^b=cf,g^e=g^1721496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36362908, #36362913, #36362931, … |
| maximal normal subgroup of | #36362908, #36362913, #36362931, … |
| maximal quotient of | #36366761, #36366763, #36366767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1384);