Finite Group Databasebeta

#28363103

order13952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1818

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D109
commutator, socleC23×C109C22×C4
FittingC2×#117×C109C2
prime radicalC24×C109C2×C4
cosocleC22×C4×C109C23
hypercenterC2×#117D109
hypocenterC109#1818
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×#117

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4581);