Finite Group Databasebeta

C22×D229⋊C8 #28412552

order14656
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D229⋊C8
unambiguous semidirect productD229⋊(C22×C8)

Splittings

derived, SylowC229 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11745021
commutator, hypocenterC229C23×C8
FrattiniC2C23×#11745021
FittingC22×C4×C229C4
socleC23×C229C2×C4
prime radicalC23×D229C4
cosocleDic229C24
LCSG ▷ C229
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

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(14656, 1620);