Finite Group Databasebeta

#11718786

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

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #430

Subgroups

subgroupG/H
centerC4C2×D52
commutatorC4×C13C22×C4
FrattiniC2×C4C22×D13
FittingC2×C13×M16C2
socleC2×C13C2×C4⋊C4
prime radicalC23×C13Q8
cosocleC2×C4×C13C23
hypercenterC2×M16D13
hypocenterC13#430
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Polycyclic presentation:

2^6,13|a^2=d,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^12,c^b=cf

Conjugacy classes & character table

142 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13115057, #13115058, #13115078, …
maximal normal subgroup of#13115057, #13115058, #13115078, …
maximal quotient of#13113588, #13113603, #13113607, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 752);