Finite Group Databasebeta

C2×Dic3368 #41003268

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

Aliases

direct productC2×Dic3368

Splittings

SylowC421 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3368
commutator, cosocleC8×C421C23
FrattiniC8C22×D421
FittingC2×C16×C421C2
socle, prime radicalC22×C421D8
hypercenterC2×C16D421
hypocenterC421C2×Q32
LCSG ▷ C8×C421 ▷ C4×C421 ▷ C2×C421 ▷ C421
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26944

Conjugacy classes & character table

6742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 977);