Finite Group Databasebeta

#28377945

order13952
automorphism?
homologyAbelianization (H1) = C4×C16 · Schur multiplier (H2) = C4

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1312

Subgroups

subgroupG/H
center, FrattiniC42C2×#89137
commutatorC2×C109C4×C16
FittingC4×C8×C109C4
socle, prime radicalC22×C109C4×C8
cosocleC4×#11724784C22
hypercenterC4×C8#89137
hypocenterC109#1312
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C42 ◁ C4×C8

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Polycyclic presentation:

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

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 19423);