Finite Group Databasebeta

#28371865

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2946

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting, prime radicalC2×AGL(1,ℤ/8)×C109C2
socleC22×C109C22×D4
cosocleC2×C4×C109C24
hypercenterC2×AGL(1,ℤ/8)D109
hypocenterC109#2946
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

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

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13343);