Finite Group Databasebeta

C22⋊C4×D92 #15676220

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×D92

Splittings

FittingC4×C22⋊C4×C23 ⋊ C2
SylowC23 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC4×C22⋊C4×C23C2
socle, cosocleC23×C23C24
prime radicalC23×D92C2
hypercenterC4×C22⋊C4D23
hypocenterC23D4×C22⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

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, 7333);