Finite Group Databasebeta

#28371496

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2884

Subgroups

subgroupG/H
centerC2C22×C22⋊Dic109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
Fitting, prime radicalC2×2−1+4×C109C2
socleC2×C109C22×C22⋊C4
cosocleC23×C109C24
hypercenterC2×2−1+4D109
hypocenterC109#2884
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×Q8 ◁ C2×2−1+4

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

2^7,109|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^108,f^b=fg,d^c=dg

Conjugacy classes & character table

1877 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12974);