Finite Group Databasebeta

C2×C4×#88100 #16796719

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×C4×#88100

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C2×C43
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C2×C4×#97
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103368);