Finite Group Databasebeta

C4×#19127666 #35401929

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#19127666

Splittings

FittingC4×C22⋊C8×C83 ⋊ C2
SylowC83 ⋊ C4×#408

Subgroups

subgroupG/H
centerC2×C42C22×D83
commutatorC22×C83C22×C42
FrattiniC22×C4C23×D83
FittingC4×C22⋊C8×C83C2
socleC23×C83C23×C4
prime radicalC22×#13050590C22
cosocleC22×C4×C83C24
hypercenterC4×C22⋊C8D83
hypocenterC83C4×#408
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

1662 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, 167093);