Finite Group Databasebeta

#28360973

order13952
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1323

Subgroups

subgroupG/H
centerC2×C4#13182006
commutatorC2×C4×C109C2×C8
FrattiniC22×C8C2×D109
FittingC22⋊C16×C109C2
socleC22×C109C22⋊C8
prime radicalC23×C109M16
cosocleC22×C8×C109C22
hypercenterC22⋊C16D109
hypocenterC109#1323
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

Conjugacy classes & character table

2198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2451);