Finite Group Databasebeta

C22×#16813568 #28403686

order14464
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16813568

Splittings

SylowC113 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23#14268632
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
FittingC22×Q16×C113C2
socle, prime radicalC23×C113D8
hypercenterC22×Q16D113
hypocenterC113C22×Q32
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

1612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 17622);