Finite Group Databasebeta

C2×#14268634 #16813635

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

Aliases

direct productC2×#14268634

Splittings

FittingC2×Q8×C113 ⋊ C2
SylowC113 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D113
commutator, cosocleC4×C113C23
FrattiniC4C22×D113
FittingC2×Q8×C113C2
socleC22×C113D4
prime radicalC2×D452C2
hypercenterC2×Q8D113
hypocenterC113C2×SD16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 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, 159);