Finite Group Databasebeta

C4×Dic1852 #44444889

order29632
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1852

Splittings

SylowC463 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D1852
commutatorC4×C463C22×C4
FrattiniC2×C4C22×D463
FittingC4×C8×C463C2
socle, prime radicalC22×C463C2×D4
cosocleC2×C4×C463C23
hypercenterC4×C8D463
hypocenterC463C4×Q16
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29632

Conjugacy classes & character table

7420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 645);