Finite Group Databasebeta

C4×D4×D172 #25256388

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

Aliases

direct productC4×D4×D172

Splittings

FittingC42×D4×C43 ⋊ C2
SylowC43 ⋊ C4×D42

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC42×D4×C43C2
socle, cosocleC23×C43C25
prime radicalC2×D4×D172C2
hypercenterC42×D4D43
hypocenterC43C4×D42
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C42×D4

4804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 329359);