Finite Group Databasebeta

C22×#16812020 #28344865

order13696
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16812020

Splittings

SylowC107 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4C2×D107
commutatorC2×C107C22×C42
FrattiniC2×C4C23×D107
FittingC22×C42×C107C2
socle, prime radicalC24×C107C2×C4
cosocleC2×C4×C107C24
hypercenterC22×C42D107
hypocenterC107C22×#97
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C23×C4 ◁ C22×C42

680 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, 12914);