Finite Group Databasebeta

#46854040

order34976
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1093 ⋊ #107

Subgroups

subgroupG/H
centerC22C22⋊D1093
commutatorC4×C1093C2×C4
FrattiniC2×C4C2×D1093
FittingC4⋊C4×C1093C2
socle, prime radicalC22×C1093D4
cosocleC2×C4×C1093C22
hypercenterC4⋊C4D1093
hypocenterC1093#107
LCSG ▷ C4×C1093 ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34976

Polycyclic presentation:

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

Conjugacy classes & character table

5474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 79);