Finite Group Databasebeta

#28360877

order13952
automorphism?
homologyAbelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1281

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic109
commutatorC22×C109C4×C8
FrattiniC2×C42C2×D109
FittingC2×#97×C109C2
socleC22×C109#95
prime radicalC23×C109C42
cosocleC2×C42×C109C22
hypercenterC2×#97D109
hypocenterC109#1281
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

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, 2355);