Finite Group Databasebeta

C2×#14268632 #16813632

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

Aliases

direct productC2×#14268632

Splittings

FittingC2×D4×C113 ⋊ C2
SylowC113 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22C22⋊D113
commutator, cosocleC4×C113C23
FrattiniC4C22×D113
FittingC2×D4×C113C2
socleC22×C113D4
hypercenterC2×D4D113
hypocenterC113C2×D8
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3616, 156);