Finite Group Databasebeta

C2×C22⋊C4×Dic26 #16022108

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C22⋊C4×Dic26

Splittings

SylowC13 ⋊ C2×Q8×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C4×C13×C22⋊C4C2
socleC24×C13C24
prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC2×C4×C22⋊C4D13
hypocenterC13C2×Q8×C22⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328757);