Finite Group Databasebeta

#28371871

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2947

Subgroups

subgroupG/H
centerC22C22×C22⋊D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#520×C109C2
socleC22×C109C22×D4
prime radicalC2×#41×C109C22
cosocleC2×C4×C109C24
hypercenter#520D109
hypocenterC109#2947
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #520

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13349);