Finite Group Databasebeta

#28361096

order13952
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1367

Subgroups

subgroupG/H
centerC2×C8D436
commutatorC4×C109C2×C16
FrattiniC4×C8C2×D109
FittingC82×C109C2
socle, prime radicalC22×C109C4⋊C8
cosocleC4×C8×C109C22
hypercenterC82D109
hypocenterC109#1367
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C82

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Polycyclic presentation:

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

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2574);