Finite Group Databasebeta

#1381×D83 #35319289

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#1381×D83

Splittings

FittingC83×#1381 ⋊ C2
SylowC83 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC2×C4D8×D83
commutatorC8×C83C2×C42
FrattiniC22×C8C22×D83
FittingC83×#1381C2
socleC22×C83C2×#107
prime radicalC23×D83Q16
cosocleC22×C8×C83C23
hypercenter#1381D83
hypocenterC83C2×#1381
LCSG ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

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, 84453);