Finite Group Databasebeta

C2×#88069 #11718841

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

Aliases

direct productC2×#88069

Splittings

SylowC13 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#6104
commutator, cosocleC8×C13C23
FrattiniC8C22×D13
FittingC2×C13×Q16C2
socle, prime radicalC22×C13D8
hypercenterC2×Q16D13
hypocenterC13C2×Q32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13116692, C4×#88069, #13116704, …
maximal normal subgroup of#13116692, C4×#88069, #13116704, …
maximal quotient ofC2×#11718084, C2×#11718156, C2×#11718081, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 807);