Finite Group Databasebeta

C2×C4×#88166 #16726938

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#88166

Splittings

FittingC2×C4×C13×D8 ⋊ C2
SylowC13 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×D8C2
socleC23×C13C22×D4
prime radicalC22×#88166C2
cosocleC2×C4×C13C25
hypercenterC2×C4×D8D13
hypocenterC13C2×C4×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033587);