Finite Group Databasebeta

C2×#88067 #11718809

order832
isoclinismisoclinic class of #88066
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#88067

Splittings

SylowC13 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#6104
commutator, cosocleC8×C13C23
FrattiniC8C22×D13
Fitting, prime radicalC2×C13×D8C2
socleC22×C13D8
hypercenterC2×D8D13
hypocenterC13C2×SD32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#88067, #13116691, #13116697, …
maximal normal subgroup ofC4×#88067, #13116691, #13116697, …
maximal quotient ofC2×#11718154, C2×#11718084, C2×#11718082, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 775);