Finite Group Databasebeta

C2×#88098 #11719085

order832
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#88098

Splittings

SylowC13 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#261
commutatorC2×C13C22×C8
FrattiniC4C22×#261
FittingC2×C8×C13C4
socleC22×C13C2×C8
prime radicalC22×D13C8
cosocle#1055C23
hypercenterC2×C8#261
hypocenterC13C2×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13129876, #13129888, #13129907, …
maximal normal subgroup of#13129876, #13129888, #13129907, …
maximal quotient ofC2×#11718258, C4×#88098, C2×#11718259, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1051);