Finite Group Databasebeta

#28365439

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2285

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
FittingC22×C42×C109C2
socle, cosocleC23×C109C24
prime radicalC24×C109C23
hypercenterC22×C42D109
hypocenterC109#2285
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

2^7,109|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,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, 6917);