Finite Group Databasebeta

#28361324

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1452

Subgroups

subgroupG/H
center, FrattiniC42C22×D109
commutator, socleC22×C109C2×C42
FittingC2×C4×C8×C109C2
prime radicalC23×C109C42
cosocleC42×C109C23
hypercenterC2×C4×C8D109
hypocenterC109#1452
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C42 ◁ C2×C4×C8

196 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=f,e^2=g,b^a=bg,c^b=cf,h^b=h^108

Conjugacy classes & character table

3512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2802);