Finite Group Databasebeta

#46801110

order34016
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC1063 ⋊ #99

Subgroups

subgroupG/H
centerC2C22⋊Dic1063
commutatorC22×C1063C2×C4
FrattiniC23C2×D1063
Fitting, prime radicalC2×D4×C1063C2
socleC2×C1063C22⋊C4
cosocleC23×C1063C22
hypercenterC2×D4D1063
hypocenterC1063#99
LCSG ▷ C22×C1063 ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8504

Polycyclic presentation:

2^5,1063|a^2=d,b^a=bc,c^a=ce,f^a=f^1062,d^b=de

Conjugacy classes & character table

5321 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 61);