Finite Group Databasebeta

C2×#13131223 #16807166

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13131223

Splittings

SylowC13 ⋊ C2×#2170

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC2×C13×#135C4
socleC22×C13C8×D4
cosocleC2×#1055C24
hypercenterC2×#135#261
hypocenterC13C2×#2170
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113815);