Finite Group Databasebeta

C4×D3356 #41001521

order26848
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D3356

Splittings

FittingC42×C839 ⋊ C2
SylowC839 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D839
commutatorC2×C839C22×C4
FrattiniC22C22×D839
FittingC42×C839C2
socle, cosocleC22×C839C23
prime radicalC2×D3356C2
hypercenterC42D839
hypocenterC839C4×D4
LCSG ▷ C2×C839 ▷ C839
UCSC1 ◁ C2×C4 ◁ C42

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13424

Conjugacy classes & character table

6724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26848, 110);