Finite Group Databasebeta

C42×#13050578 #35402874

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#13050578

Splittings

SylowC83 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D83
commutatorC4×C83C22×C42
FrattiniC22×C4C23×D83
FittingC42×D4×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83C23
cosocleC22×C4×C83C24
hypercenterC42×D4D83
hypocenterC83C42×SD16
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 168038);