Finite Group Databasebeta

← Prev (#25255876) Next (#25255878) →

D4×C4⋊C4×D43 #25255877

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×C4⋊C4×D43

Splittings

FittingD4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingD4×C4⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC22×D4×D43C22
hypercenterD4×C4⋊C4D43
hypocenterC43C2×D4×C4⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ D4×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328848);