Finite Group Databasebeta

#28364934

order13952
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ Q8×C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×D109
commutatorC2×C109C22×C16
FittingC4⋊C16×C109C2
socle, prime radicalC22×C109C22×C8
cosocleC2×C8×C109C23
hypercenterC4⋊C16D109
hypocenterC109Q8×C16
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ C4⋊C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13952

Polycyclic presentation:

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

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6412);