Finite Group Databasebeta

C22⋊C4×D733 #37553124

order23456
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D733

Splittings

FittingC22⋊C4×C733 ⋊ C2
SylowC733 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D733
commutatorC2×C733C22×C4
FittingC22⋊C4×C733C2
socle, cosocleC22×C733C23
prime radicalC23×D733C2
hypercenterC22⋊C4D733
hypocenterC733C2×C22⋊C4
LCSG ▷ C2×C733 ▷ C733
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5864

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23456, 96);