Finite Group Databasebeta

#107×D419 #41000393

order26816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#107×D419

Splittings

Fitting#107×C419 ⋊ C2
SylowC419 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D419
commutatorC4×C419C22×C4
FrattiniC2×C4C22×D419
Fitting#107×C419C2
socleC22×C419C2×D4
prime radicalC22×D419D4
cosocleC2×C4×C419C23
hypercenter#107D419
hypocenterC419C2×#107
LCSG ▷ C4×C419 ▷ C2×C419 ▷ C419
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

2954 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 581);