Finite Group Databasebeta

C2×C4×#88069 #16016192

order3328
isoclinismisoclinic class of #88066
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×#88069

Splittings

SylowC13 ⋊ C2×C4×Q32

Subgroups

subgroupG/H
centerC22×C4#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C4×C13×Q16C2
socle, prime radicalC23×C13C2×D8
cosocleC2×C8×C13C24
hypercenterC2×C4×Q16D13
hypocenterC13C2×C4×Q32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322841);