Finite Group Databasebeta

D13×#107 #11718540

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

Aliases

direct productD13×#107

Splittings

FittingC13×#107 ⋊ C2
SylowC13 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22D4×D13
commutatorC4×C13C22×C4
FrattiniC2×C4C22×D13
FittingC13×#107C2
socleC22×C13C2×D4
prime radicalC22×D13D4
cosocleC2×C4×C13C23
hypercenter#107D13
hypocenterC13C2×#107
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×#357, D13×#358, #13116545, …
maximal normal subgroup ofD13×#357, D13×#358, #13116545, …
maximal quotient ofD13×#335, #13113593, #13113609, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 506);