Finite Group Databasebeta

C2×Dic452 #16813640

order3616
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic452

Splittings

SylowC113 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D452
commutator, cosocleC4×C113C23
FrattiniC4C22×D113
FittingC2×C8×C113C2
socle, prime radicalC22×C113D4
hypercenterC2×C8D113
hypocenterC113C2×Q16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3616, 164);