Finite Group Databasebeta

C22×Dic463⋊C4 #44445243

order29632
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×Dic463⋊C4

Splittings

SylowC463 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D463
commutatorC2×C463C23×C4
FrattiniC22C23×D463
FittingC23×C4×C463C2
socle, prime radicalC24×C463C22
cosocleC22×C463C24
hypercenterC23×C4D463
hypocenterC463C22×C4⋊C4
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C24 ◁ C23×C4

418 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, 999);