Finite Group Databasebeta

#466×D271 #46845928

order34688
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#466×D271

Splittings

Fitting#466×C271 ⋊ C2
SylowC271 ⋊ C2×#466

Subgroups

subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#466×C271C2
socleC22×C271C22×D4
hypercenter#466D271
hypocenterC271C2×#466
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8672

Conjugacy classes & character table

3014 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 14074);