Finite Group Databasebeta

C2×#88064 #11718797

order832
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#88064

Splittings

SylowC13 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#6103
commutatorC22×C13C22×C4
FrattiniC2×C4C22×D13
FittingC2×C13×M16C2
socleC22×C13C22⋊C4
prime radicalC23×C13C2×C4
cosocleC2×C4×C13C23
hypercenterC2×M16D13
hypocenterC13C2×#101
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

142 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13114631, C4×#88064, #13114758, …
maximal normal subgroup of#13114631, C4×#88064, #13114758, …
maximal quotient ofC2×#11718061, #13113159, #13113165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 763);