Finite Group Databasebeta

#1380×D83 #35319279

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct product#1380×D83

Splittings

FittingC83×#1380 ⋊ C2
SylowC83 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC23D8×D83
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC83×#1380C2
socleC23×C83C2×D8
prime radicalC23×D83D8
cosocleC22×C8×C83C23
hypercenter#1380D83
hypocenterC83C2×#1380
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84443);