Finite Group Databasebeta

C2×Dic242 #14515433

order1936
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic242
unambiguous semidirect product(C2×C121)⋊Q8

Splittings

SylowC121 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22C2×D121
commutator, cosocleC2×C121C23
FrattiniC2×C11C22×D11
FittingC2×C4×C121C2
socle, prime radicalC22×C11C2×D11
hypercenterC2×C4D121
hypocenterC121C2×Q8
LCSG ▷ C2×C121 ▷ C121
UCSC1 ◁ C22 ◁ C2×C4

57 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1936

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 27);