Finite Group Databasebeta

C2×#13128035 #16769513

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

Aliases

direct productC2×#13128035

Splittings

FittingC2×C4×C13×#41 ⋊ C2
SylowC13 ⋊ C2×#3428

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC2×C4×C13×#41C2
socleC23×C13C25
prime radicalC22×#41×D13C2
cosocleC22×C13C26
hypercenterC2×C4×#41D13
hypocenterC13C2×#3428
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

11534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076162);