Finite Group Databasebeta

C2×C4×Dic926 #44445258

order29632
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic926

Splittings

SylowC463 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D463
commutatorC2×C463C23×C4
FrattiniC22C23×D463
FittingC2×C42×C463C2
socle, prime radicalC23×C463C23
cosocleC22×C463C24
hypercenterC2×C42D463
hypocenterC463C2×C4×Q8
LCSG ▷ C2×C463 ▷ C463
UCSC1 ◁ C22×C4 ◁ C2×C42

298 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, 1014);