Finite Group Databasebeta

C2×C4×#88240 #16808016

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#88240

Splittings

SylowC13 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C23×C4
prime radicalC22×#6131C22
cosocleC2×Dic13C25
hypercenterC2×C4×Q8#261
hypocenterC13C2×C4×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114665);