Finite Group Databasebeta

C4×#19127424 #35294907

order21248
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#19127424

Splittings

FittingC4×C22⋊C8×C83 ⋊ C2
SylowC83 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4(C2×D83)⋊C4
commutatorC22×C83C2×C4×C8
FrattiniC23×C4C22×D83
FittingC4×C22⋊C8×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC24×D83C2×C4
cosocleC23×C4×C83C23
hypercenterC4×C22⋊C8D83
hypocenterC83C4×#323
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 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, 60071);