Finite Group Databasebeta

C2×Dic2672 #36326443

order21376
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic2672

Splittings

SylowC167 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D2672
commutator, cosocleC16×C167C23
FrattiniC16C22×D167
FittingC2×C32×C167C2
socle, prime radicalC22×C167D16
hypercenterC2×C32D167
hypocenterC167C2×Q64
LCSG ▷ C16×C167 ▷ C8×C167 ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21376

Conjugacy classes & character table

5350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 6815);