Finite Group Databasebeta

C2×Dic3544 #43248145

order28352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3544

Splittings

SylowC443 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3544
commutator, cosocleC8×C443C23
FrattiniC8C22×D443
FittingC2×C16×C443C2
socle, prime radicalC22×C443D8
hypercenterC2×C16D443
hypocenterC443C2×Q32
LCSG ▷ C8×C443 ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28352

Conjugacy classes & character table

7094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 977);