Finite Group Databasebeta

#468×D107 #28346045

order13696
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#468×D107

Splittings

Fitting#468×C107 ⋊ C2
SylowC107 ⋊ C2×#468

Subgroups

subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#468×C107C2
socleC22×C107C22×D4
prime radical#121×D107C2
hypercenter#468D107
hypocenterC107C2×#468
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3424

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 14094);