Finite Group Databasebeta

#46854072

order34976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC1093 ⋊ C4×Q8

Subgroups

subgroupG/H
center, FrattiniC22C22×D1093
commutatorC2×C1093C22×C4
FittingC4⋊C4×C1093C2
socle, prime radical, cosocleC22×C1093C23
hypercenterC4⋊C4D1093
hypocenterC1093C4×Q8
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C22 ◁ C4⋊C4

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34976

Polycyclic presentation:

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

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 111);