Finite Group Databasebeta

#416×D107 #28344953

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

Aliases

direct product#416×D107

Splittings

Fitting#416×C107 ⋊ C2
SylowC107 ⋊ C2×#416

Subgroups

subgroupG/H
centerC2×C4D4×D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
Fitting#416×C107C2
socleC22×C107C22×D4
prime radicalC2×#41×D107C2
cosocleC2×C4×C107C24
hypercenter#416D107
hypocenterC107C2×#416
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

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, 13002);