Finite Group Databasebeta

C2×C4×#88059 #15861015

order3328
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#88059

Splittings

SylowC13 ⋊ C2×C4×#108

Subgroups

subgroupG/H
centerC2×C42D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C2×C4⋊C4
prime radicalC24×C13C2×Q8
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×C4×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 167664);