Finite Group Databasebeta

C2×C4×#16864638 #46844773

order34688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#16864638

Splittings

SylowC271 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D271
commutatorC2×C271C22×C42
FrattiniC2×C4C23×D271
FittingC22×C42×C271C2
socleC23×C271C22×C4
prime radicalC24×C271C2×C4
cosocleC2×C4×C271C24
hypercenterC22×C42D271
hypocenterC271C2×C4×M16
LCSG ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C42 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17344

Conjugacy classes & character table

8720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34688, 12919);