Finite Group Databasebeta

C2×#13116718 #16016320

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13116718

Splittings

FittingC2×C4×C13×C16 ⋊ C2
SylowC13 ⋊ C2×#2178

Subgroups

subgroupG/H
centerC2×C8D104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C4×C13×C16C2
socleC22×C13C4×D8
prime radicalC2×#11718565C2
cosocleC2×C8×C13C24
hypercenterC2×C4×C16D13
hypocenterC13C2×#2178
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322969);