Finite Group Databasebeta

C2×#88062 #11718784

order832
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#88062

Splittings

SylowC13 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D13
commutatorC4×C13C22×C4
FrattiniC2×C4C22×D13
FittingC2×C13×M16C2
socleC22×C13C4⋊C4
prime radicalC23×C13Q8
cosocleC2×C4×C13C23
hypercenterC2×M16D13
hypocenterC13C2×#108
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13114714, #13114716, #13114719, …
maximal normal subgroup of#13114714, #13114716, #13114719, …
maximal quotient ofC2×#11718072, C2×#11718071, #13113582, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 750);