Finite Group Databasebeta

C2×#20292402 #28338050

order13696
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20292402

Splittings

SylowC107 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D107
commutatorC2×C107C2×C4×C8
FrattiniC2×C8C22×D107
FittingC22×C16×C107C2
socle, prime radicalC23×C107C2×C8
cosocleC2×C8×C107C23
hypercenterC22×C16D107
hypocenterC107C2×#346
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C8 ◁ C22×C16

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13696

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6099);