Finite Group Databasebeta

C22×#16813697 #28407537

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

Aliases

direct productC22×#16813697

Splittings

SylowC113 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C4C2×#90673
commutatorC2×C113C23×C8
FrattiniC4C23×#90673
FittingC22×C8×C113C4
socleC23×C113C2×C8
prime radicalC23×D113C8
cosocle#11744751C24
hypercenterC22×C8#90673
hypocenterC113C22×M32
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ C22×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21473);