Finite Group Databasebeta

#102×C22⋊D83 #35419806

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#102×C22⋊D83

Splittings

FittingC22×#102×C83 ⋊ C2
SylowC83 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC22×#102×C83C2
socleC23×C83C22×D4
prime radicalC2×D4×C22⋊D83C2
cosocleC22×C4×C83C24
hypercenterC22×#102D83
hypocenterC83D4×#102
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 184970);