Finite Group Databasebeta

C4×Dic463⋊C4 #44444646

order29632
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×Dic463⋊C4

Splittings

SylowC463 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D463
commutatorC2×C463C2×C42
FrattiniC23C22×D463
FittingC2×C42×C463C2
socle, prime radical, cosocleC23×C463C23
hypercenterC2×C42D463
hypocenterC463C4×C4⋊C4
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29632

Conjugacy classes & character table

7432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 402);