Finite Group Databasebeta

#41×Dic421 #41003311

order26944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic421

Splittings

SylowC421 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D421
commutatorC2×C421C23×C4
FrattiniC22C23×D421
Fitting, prime radicalC2×#41×C421C2
socle, cosocleC22×C421C24
hypercenterC2×#41D421
hypocenterC421C4×#41
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

4240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1020);