Finite Group Databasebeta

#1830×D83 #35404268

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

Aliases

direct product#1830×D83

Splittings

FittingC83×#1830 ⋊ C2
SylowC83 ⋊ C2×#1830

Subgroups

subgroupG/H
centerC2#381×D83
commutatorC23×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1830C2
socleC2×C83C2×#381
prime radicalC23×D83C22×C4
cosocleC22×C4×C83C24
hypercenter#1830D83
hypocenterC83C2×#1830
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1830

1218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2656

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 169432);