Finite Group Databasebeta

C2×#20292387 #28336167

order13696
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20292387

Splittings

SylowC107 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4D428
commutatorC4×C107C2×C42
FrattiniC22×C4C22×D107
FittingC22×C42×C107C2
socleC23×C107C22⋊C4
prime radicalC24×C107D4
cosocleC22×C4×C107C23
hypercenterC22×C42D107
hypocenterC107C2×#339
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

3448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 4216);