Finite Group Databasebeta

C22⋊C4×Dic46 #15676232

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic46

Splittings

SylowC23 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC4×C22⋊C4×C23C2
socle, cosocleC23×C23C24
prime radicalC24×C23C23
hypercenterC4×C22⋊C4D23
hypocenterC23Q8×C22⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7345);