Finite Group Databasebeta

C22⋊C4×D839 #41001507

order26848
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D839

Splittings

FittingC22⋊C4×C839 ⋊ C2
SylowC839 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D839
commutatorC2×C839C22×C4
FittingC22⋊C4×C839C2
socle, cosocleC22×C839C23
prime radicalC23×D839C2
hypercenterC22⋊C4D839
hypocenterC839C2×C22⋊C4
LCSG ▷ C2×C839 ▷ C839
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6712

Conjugacy classes & character table

4210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 96);