Finite Group Databasebeta

#11718136

order832
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #331

Subgroups

subgroupG/H
centerC22C22⋊Dic13
commutatorC2×C4×C13C2×C4
FrattiniC42C2×D13
Fitting, prime radicalC13×#127C2
socleC22×C13C22⋊C4
cosocleC42×C13C22
hypercenter#127D13
hypocenterC13#331
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #127

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Polycyclic presentation:

2^6,13|a^2=c,c^2=e,d^2=f,b^a=bd,d^a=def,g^a=g^12,c^b=ce,d^b=df

Conjugacy classes & character table

103 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13112980, #13112981, D13×#331, …
maximal normal subgroup of#13112980, #13112981, D13×#331, …
maximal quotient of#13112657, #13112719, #13112873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 102);