Finite Group Databasebeta

#1388×D83 #35319333

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#1388×D83

Splittings

FittingC83×#1388 ⋊ C2
SylowC83 ⋊ C2×#1388

Subgroups

subgroupG/H
centerC4#102×D83
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC83×#1388C2
socleC2×C83C2×#340
prime radicalC23×D83Q16
cosocleC22×C8×C83C23
hypercenter#1388D83
hypocenterC83C2×#1388
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1388

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84497);