Finite Group Databasebeta

C2×#20292467 #28338765

order13696
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20292467

Splittings

SylowC107 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22#16812050
commutator, cosocleC16×C107C23
FrattiniC16C22×D107
FittingC2×Q32×C107C2
socle, prime radicalC22×C107D16
hypercenterC2×Q32D107
hypocenterC107C2×Q64
LCSG ▷ C16×C107 ▷ C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6814);