Finite Group Databasebeta

#100×C22⋊D83 #35419752

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#100×C22⋊D83

Splittings

FittingC22×#100×C83 ⋊ C2
SylowC83 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D83
commutatorC23×C83C23×C4
FrattiniC22×C4C23×D83
FittingC22×#100×C83C2
socleC22×C83C22×C22⋊C4
prime radicalC2×D4×C22⋊D83C2
cosocleC22×C4×C83C24
hypercenterC22×#100D83
hypocenterC83D4×#100
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1859 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 184916);