Finite Group Databasebeta

C8×Dic842 #41002965

order26944
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic842

Splittings

SylowC421 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D421
commutatorC2×C421C22×C8
FrattiniC2×C4C22×D421
FittingC4×C8×C421C2
socle, prime radicalC22×C421C22×C4
cosocleC2×C4×C421C23
hypercenterC4×C8D421
hypocenterC421C8×Q8
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C2×C8 ◁ C4×C8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26944

Conjugacy classes & character table

6760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 674);