Finite Group Databasebeta

C2×#13123747 #16727233

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123747

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C2×#2956

Subgroups

subgroupG/H
centerC2×C4C22×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×M16C2
socleC22×C13C2×C4×D4
prime radicalC2×#11719453C2
cosocleC2×C4×C13C25
hypercenterC2×C4×M16D13
hypocenterC13C2×#2956
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×C4×M16

2674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033882);