Finite Group Databasebeta

C22×#16813628 #28405278

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16813628

Splittings

FittingC23×C8×C113 ⋊ C2
SylowC113 ⋊ C22×#131

Subgroups

subgroupG/H
centerC22×C8C2×D113
commutatorC2×C113C24×C4
FrattiniC4C24×D113
FittingC23×C8×C113C2
socleC23×C113C22×C4
prime radicalC22×#14268647C2
cosocleC4×C113C25
hypercenterC23×C8D113
hypocenterC113C22×#131
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C8 ◁ C23×C8

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

3664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19214);