Finite Group Databasebeta

#28365624

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

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2311

Subgroups

subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting, prime radicalC22×#41×C109C2
socle, cosocleC23×C109C24
hypercenterC22×#41D109
hypocenterC109#2311
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×#41

880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

2^7,109|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^108,c^b=ce

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7102);