Finite Group Databasebeta

C2×#13115623 #15866484

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

Aliases

direct productC2×#13115623

Splittings

SylowC13 ⋊ C2×#1953

Subgroups

subgroupG/H
centerC2×C4#88193
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#430C2
socleC22×C13#389
prime radicalC24×C13C2×Q8
cosocleC22×C4×C13C24
hypercenterC2×#430D13
hypocenterC13C2×#1953
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 173133);