Finite Group Databasebeta

C2×C4×Dic122 #16840227

order3904
isoclinismisoclinic class of Dic122
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic122

Splittings

SylowC61 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D61
commutatorC2×C61C23×C4
FrattiniC22C23×D61
FittingC2×C42×C61C2
socle, prime radicalC23×C61C23
cosocleC22×C61C24
hypercenterC2×C42D61
hypocenterC61C2×C4×Q8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1014);