Finite Group Databasebeta

C22×#16813718 #28407821

order14464
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16813718

Splittings

SylowC113 ⋊ C22×M32

Subgroups

subgroupG/H
centerC23C2×#11744762
commutatorC2×C113C23×C8
FrattiniC2C23×#11744762
Fitting, prime radicalC24×C113C8
socleC23×C113C2×C8
cosocle#11744753C24
hypercenterC24#11744762
hypocenterC113C22×M32
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C24

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21757);