Finite Group Databasebeta

C2×C4×#88251 #16769520

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×C4×#88251

Splittings

FittingC22×C4×D4×C13 ⋊ C2
SylowC13 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC22×C4×D4×C13C2
socleC23×C13C25
prime radicalC22×#88251C2
cosocleC22×C13C26
hypercenterC22×C4×D4D13
hypocenterC13C2×C4×H(5,𝔽2)
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

12378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076169);