Finite Group Databasebeta

#28361165

order13952
automorphism?
homologyAbelianization (H1) = C4×C16 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1397

Subgroups

subgroupG/H
center, FrattiniC2×C16C2×D109
commutatorC2×C109C4×C16
FittingC2×C32×C109C2
socle, prime radicalC22×C109C2×C16
cosocleC2×C16×C109C22
hypercenterC2×C32D109
hypocenterC109#1397
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C16 ◁ C2×C32

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Polycyclic presentation:

2^7,109|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^108

Conjugacy classes & character table

3536 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2643);