Finite Group Databasebeta

#28379999

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #3407

Subgroups

subgroupG/H
center, FrattiniC4C23×#89137
commutator, socleC2×C109C23×C8
Fitting, prime radicalC2×#41×C109C4
cosocle#11724784C24
hypercenterC2×#41#89137
hypocenterC109#3407
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C2×#41

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21477);