Finite Group Databasebeta

C2×C4×(C2×#261)⋊C4 #16791504

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×(C2×#261)⋊C4

Splittings

FittingC22×C42×C13 ⋊ C4
SylowC13 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C2×C43
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC22×C42#261
hypocenterC13C2×C4×#95
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42

4462 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, 1098153);