Finite Group Databasebeta

Q32×D421 #41003266

order26944
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ32×D421

Splittings

FittingQ32×C421 ⋊ C2
SylowC421 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC2D8×D421
commutator, cosocleC8×C421C23
FrattiniC8C22×D421
FittingQ32×C421C2
socleC2×C421C2×D8
prime radicalC2×D421D8
hypercenterQ32D421
hypocenterC421C2×Q32
LCSG ▷ C8×C421 ▷ C4×C421 ▷ C2×C421 ▷ C421
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

2332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 975);