Finite Group Databasebeta

#28379592

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ C2×#405

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C22×C42
FrattiniC22C23×#89137
Fitting#117×C109C4
socleC22×C109C23×C4
prime radicalC23×D109C2×C4
cosocleC2×Dic109C24
hypercenter#117#89137
hypocenterC109C2×#405
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ #117

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Polycyclic presentation:

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

Conjugacy classes & character table

620 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21070);