Finite Group Databasebeta

#28379710

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

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2920

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutator, socleC22×C109C23×C4
FrattiniC22C23×#89137
FittingC2×C42×C109C4
prime radicalC23×D109C2×C4
cosocleC2×Dic109C24
hypercenterC2×C42#89137
hypocenterC109#2920
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×C42

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

2^7,109|a^2=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^33,h^b=h^108,h^f=h^108

Conjugacy classes & character table

920 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21188);