Finite Group Databasebeta

C2×#13129663 #16778964

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#13129663

Splittings

FittingC2×C13×C4⋊C8 ⋊ C4
SylowC13 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC4×C13C2×C4×C8
FrattiniC42C22×#261
FittingC2×C13×C4⋊C8C4
socleC23×C13#95
prime radicalC23×D13C22⋊C4
cosocleC42×D13C23
hypercenterC2×C4⋊C8#261
hypocenterC13C2×#1276
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1085613);