Finite Group Databasebeta

#11719128

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

Aliases

No aliases for this group.

Splittings

SylowC13 ⋊ #432

Subgroups

subgroupG/H
center, FrattiniC22C22×#261
commutator, socleC22×C13C22×C4
FittingC22×C4×C13C4
prime radicalC23×C13C2×C4
cosocleC2×Dic13C23
hypercenterC22×C4#261
hypocenterC13#432
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Polycyclic presentation:

2^6,13|a^2=d,c^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^8,g^d=g^12

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13129687, #13129694, #13129704, …
maximal normal subgroup of#13129687, #13129694, #13129704, …
maximal quotient of#13130553, #13130562, #13130621, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1094);