Finite Group Databasebeta

C4⋊Q8×D421 #41003381

order26944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊Q8×D421

Splittings

FittingC4⋊Q8×C421 ⋊ C2
SylowC421 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C23×D421
commutator, socle, cosocleC22×C421C24
FittingC4⋊Q8×C421C2
prime radicalC22×D421C23
hypercenterC4⋊Q8D421
hypocenterC421C2×C4⋊Q8
LCSG ▷ C22×C421 ▷ C421
UCSC1 ◁ C22 ◁ C4⋊Q8

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

2968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 1090);