Finite Group Databasebeta

C4×#19127478 #35319231

order21248
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C42

Aliases

direct productC4×#19127478

Splittings

SylowC83 ⋊ C4×#347

Subgroups

subgroupG/H
centerC42C4×Dic83
commutatorC4×C83C43
FrattiniC22×C8C22×D83
FittingC4×M32×C83C2
socleC22×C83C2×#97
prime radicalC23×C83C2×M16
cosocleC22×C8×C83C23
hypercenterC4×M32D83
hypocenterC83C4×#347
LCSG ▷ C4×C83 ▷ C83
UCSC1 ◁ C42 ◁ C4×M32

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84395);