Finite Group Databasebeta

#2897×D83 #36267948

order21248
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#2897×D83

Splittings

FittingC83×#2897 ⋊ C2
SylowC83 ⋊ C2×#2897

Subgroups

subgroupG/H
centerC22C22×D4×D83
commutatorC4×C83C24×C4
FrattiniC2×C4C24×D83
FittingC83×#2897C2
socleC22×C83C23×D4
prime radicalC2×H(5,𝔽2)×D83C2
cosocleC2×C4×C83C25
hypercenter#2897D83
hypocenterC83C2×#2897
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

5226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

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, 1033112);