Finite Group Databasebeta

#322×D113 #28388848

order14464
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×D113

Splittings

Fitting#322×C113 ⋊ C2
SylowC113 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D113
commutatorC2×C113C2×C4×C8
Fitting#322×C113C2
socleC22×C113C2×C42
prime radicalC22×D113C42
cosocleC42×C113C23
hypercenter#322D113
hypocenterC113C2×#322
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C42 ◁ #322

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 2784);