Finite Group Databasebeta

C2×#13115470 #15865289

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13115470

Splittings

SylowC13 ⋊ C2×#1927

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C4×C13×C4⋊C4C2
socle, prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#1927
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171938);