Finite Group Databasebeta

#28361230

order13952
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1422

Subgroups

subgroupG/H
centerC16D436
commutatorC4×C109C2×C16
FrattiniC2×C16C2×D109
FittingC4×C16×C109C2
socleC2×C109C4⋊C16
prime radicalC22×C109M32
cosocleC2×C16×C109C22
hypercenterC4×C16D109
hypocenterC109#1422
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C16 ◁ C2×C16 ◁ C4×C16

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

2^7,109|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,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, 2708);