Finite Group Databasebeta

#46854036

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

Aliases

No aliases for this group.

Splittings

SylowC1093 ⋊ C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D1093
commutatorC2×C1093C2×C8
FittingC2×C8×C1093C2
socle, prime radicalC22×C1093C2×C4
cosocleC2×C4×C1093C22
hypercenterC2×C8D1093
hypocenterC1093C4⋊C8
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C2×C4 ◁ C2×C8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34976

Polycyclic presentation:

2^5,1093|a^2=d,b^2=c,d^2=e,b^a=bc,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, 75);