Finite Group Databasebeta

C4×Dic226 #16813588

order3616
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic226

Splittings

SylowC113 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D113
commutatorC2×C113C22×C4
FrattiniC22C22×D113
FittingC42×C113C2
socle, prime radical, cosocleC22×C113C23
hypercenterC42D113
hypocenterC113C4×Q8
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3616, 112);