Finite Group Databasebeta

C2×#11718570 #13127967

order1664
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11718570

Splittings

FittingC2×C13×M32 ⋊ C2
SylowC13 ⋊ C2×#510

Subgroups

subgroupG/H
centerC22C2×D104
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC2×C13×M32C2
socleC22×C13C2×D8
prime radicalC2×#88158C2
hypercenterC2×M32D13
hypocenterC13C2×#510
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

Relationships

maximal subgroup of#15780052, #15780054, #15780073, …
maximal normal subgroup of#15780052, #15780054, #15780073, …
maximal quotient ofC2×#13116557, C2×#13116549, C2×#13116624, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 17641);