Finite Group Databasebeta

C4×#19127556 #35325610

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#19127556

Splittings

FittingC2×C4×C22⋊C4×C83 ⋊ C2
SylowC83 ⋊ C4×#379

Subgroups

subgroupG/H
centerC23×C4C22×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×D83C22
hypercenterC2×C4×C22⋊C4D83
hypocenterC83C4×#379
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

6734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 90774);