Finite Group Databasebeta

C4×#19127698 #35402156

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

Aliases

direct productC4×#19127698

Splittings

FittingC22×C4×C8×C83 ⋊ C2
SylowC83 ⋊ C4×#416

Subgroups

subgroupG/H
centerC2×C42D332
commutatorC4×C83C22×C42
FrattiniC22×C4C23×D83
FittingC22×C4×C8×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050590C22
cosocleC22×C4×C83C24
hypercenterC22×C4×C8D83
hypocenterC83C4×#416
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

5360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 167320);