Finite Group Databasebeta

C22×#16814643 #28411928

order14656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#16814643

Splittings

FittingC23×C4×C229 ⋊ C2
SylowC229 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D229
commutatorC2×C229C23×C4
FrattiniC22C23×D229
FittingC23×C4×C229C2
socleC24×C229C22
prime radicalC24×D229C2
cosocleC22×C229C24
hypercenterC23×C4D229
hypocenterC229C22×C22⋊C4
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 996);