Finite Group Databasebeta

#123×#90673 #28407039

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#123×#90673

Splittings

Fitting#123×C113 ⋊ C4
SylowC113 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
Fitting#123×C113C4
prime radicalC2×D4×D113C22
cosocleC22×D113C24
hypercenter#123#90673
hypocenterC113C4×#123
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #123

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20975);