Finite Group Databasebeta

#46854066

order34976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC1093 ⋊ #117

Subgroups

subgroupG/H
centerC2×C4C2×D1093
commutatorC2×C1093C22×C4
FrattiniC22C22×D1093
FittingC22×C4×C1093C2
socle, cosocleC22×C1093C23
prime radicalC23×C1093C22
hypercenterC22×C4D1093
hypocenterC1093#117
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C2×C4 ◁ C22×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17488

Polycyclic presentation:

2^5,1093|a^2=e,c^2=d,b^a=bd,f^a=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, 105);