Finite Group Databasebeta

#413×D107 #28344932

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

Aliases

direct product#413×D107

Splittings

Fitting#413×C107 ⋊ C2
SylowC107 ⋊ C2×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×D107
commutatorC22×C107C23×C4
FrattiniC2×C4C23×D107
Fitting#413×C107C2
socleC2×C107C22×C22⋊C4
prime radicalC2×#41×D107C2
cosocleC2×C4×C107C24
hypercenter#413D107
hypocenterC107C2×#413
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1712

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 12981);