Finite Group Databasebeta

#46854046

order34976
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

FittingC16×C1093 ⋊ C2
SylowC1093 ⋊ M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D1093
commutator, socleC2×C1093C2×C8
FittingC16×C1093C2
prime radicalC2×D1093C8
cosocleC8×C1093C22
hypercenterC16D1093
hypocenterC1093M32
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C8 ◁ C16

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17488

Polycyclic presentation:

2^5,1093|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^1092

Conjugacy classes & character table

8756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 85);