Finite Group Databasebeta

#28376235

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #3428

Subgroups

subgroupG/H
centerC2×C4C23×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
Fitting, prime radicalC22×#41×C109C2
socle, cosocleC22×C109C25
hypercenterC22×#41D109
hypocenterC109#3428
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×#41

1540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

2^7,109|a^2=g,e^2=f,b^a=bf,d^a=df,h^a=h^108,c^b=cf

Conjugacy classes & character table

2228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17713);