Finite Group Databasebeta

C2×C42×D332 #35562597

order21248
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C42×D332

Splittings

FittingC2×C43×C83 ⋊ C2
SylowC83 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC22×C42C2×D83
commutatorC2×C83C23×C42
FrattiniC23C24×D83
FittingC2×C43×C83C2
socleC24×C83C24
prime radicalC23×D332C22
cosocleC23×C83C25
hypercenterC2×C43D83
hypocenterC83C2×C42×D4
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C42 ◁ C2×C43

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

5408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 327761);