Finite Group Databasebeta

#1827×D83 #35404244

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

Aliases

direct product#1827×D83

Splittings

FittingC83×#1827 ⋊ C2
SylowC83 ⋊ C2×#1827

Subgroups

subgroupG/H
centerC4#117×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1827C2
socleC2×C83C2×#381
prime radicalC2×#41×D83C22
cosocleC22×C4×C83C24
hypercenter#1827D83
hypocenterC83C2×#1827
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ #117 ◁ #1827

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1328

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, 169408);