Finite Group Databasebeta

C2×C4×#88124 #16021410

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×C4×#88124

Splittings

SylowC13 ⋊ C2×C4×#125

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C43×C13C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×C43D13
hypocenterC13C2×C4×#125
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C43

2622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328059);