Finite Group Databasebeta

#28379622

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2880

Subgroups

subgroupG/H
center, FrattiniC22C23×#89137
commutator, socleC22×C109C23×C4
FittingC2×#41×C109C4
prime radicalC2×#41×D109C2
cosocleC2×Dic109C24
hypercenterC2×#41#89137
hypocenterC109#2880
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×#41

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

2^7,109|a^2=f,f^2=g,b^a=be,h^a=h^33,h^b=h^108,d^c=dg,h^f=h^108

Conjugacy classes & character table

590 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21100);