Finite Group Databasebeta

#39907411

order26032
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1627 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1627
commutator, cosocleC4×C1627C22
FrattiniC4C2×D1627
Fitting, prime radicalD4×C1627C2
socleC2×C1627D4
hypercenterD4D1627
hypocenterC1627SD16
LCSG ▷ C4×C1627 ▷ C2×C1627 ▷ C1627
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13016

Polycyclic presentation:

2^4,1627|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1626,c^b=cd

Conjugacy classes & character table

4072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26032, 28);