Finite Group Databasebeta

C2×C4×C22⋊#1057 #16796866

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C22⋊#1057

Splittings

SylowC13 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC24×C4×C13C4
socleC24×C13C22×C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC24×C4#261
hypocenterC13C2×C4×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1103515);