Finite Group Databasebeta

#28371599

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

Aliases

No aliases for this group.

Splittings

Fitting#424×C109 ⋊ C2
SylowC109 ⋊ #2906

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D109
commutator, socleC22×C109C23×C4
Fitting#424×C109C2
prime radicalC2×#13182029C22
cosocleC2×C4×C109C24
hypercenter#424D109
hypocenterC109#2906
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ #424

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

Conjugacy classes & character table

1562 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13077);