Finite Group Databasebeta

#407×D107 #28344894

order13696
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#407×D107

Splittings

Fitting#407×C107 ⋊ C2
SylowC107 ⋊ C2×#407

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#407×C107C2
prime radicalC24×D107C4
cosocleC2×C4×C107C24
hypercenter#407D107
hypocenterC107C2×#407
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #407

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1712

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12943);