Finite Group Databasebeta

C4×#19127503 #35319609

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#19127503

Splittings

FittingC2×C4×C16×C83 ⋊ C2
SylowC83 ⋊ C4×#357

Subgroups

subgroupG/H
centerC22×C4D664
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC2×C4×C16×C83C2
socleC23×C83C2×D8
prime radicalC22×D664C22
cosocleC22×C8×C83C23
hypercenterC2×C4×C16D83
hypocenterC83C4×#357
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

5336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84773);