Finite Group Databasebeta

#28360982

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

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #1327

Subgroups

subgroupG/H
centerC4#16812613
commutatorC2×C4×C109C2×C8
FrattiniC2×M16C2×D109
Fitting#349×C109C2
socleC2×C109#324
prime radicalC23×C109M16
cosocleC2×M16×C109C22
hypercenter#349D109
hypocenterC109#1327
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Polycyclic presentation:

2^7,109|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=deg,h^b=h^108,d^c=dg

Conjugacy classes & character table

1214 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2460);