Finite Group Databasebeta

#28371964

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC109 ⋊ #2960

Subgroups

subgroupG/H
centerC2×C8C22×D109
commutator, socleC22×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#405×C109C2
prime radicalC23×C109C22×C4
cosocleC2×C4×C109C24
hypercenter#405D109
hypocenterC109#2960
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C8 ◁ #405

364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Polycyclic presentation:

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

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13442);