Finite Group Databasebeta

C2×C4×#41×D13 #16769490

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

Aliases

direct productC2×C4×#41×D13

Splittings

FittingC2×C4×C13×#41 ⋊ C2
SylowC13 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC2×C4×C13×#41C2
socleC23×C13C25
prime radicalC22×#41×D13C2
cosocleC22×C13C26
hypercenterC2×C4×#41D13
hypocenterC13C22×C4×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076139);