Finite Group Databasebeta

#431×D109 #28371644

order13952
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#431×D109

Splittings

Fitting#431×C109 ⋊ C2
SylowC109 ⋊ C2×#431

Subgroups

subgroupG/H
centerC42C22×D109
commutatorC2×C109C23×C8
FrattiniC2×C4C23×D109
Fitting#431×C109C2
socleC22×C109C23×C4
prime radicalC23×D109C2×C4
cosocleC2×C4×C109C24
hypercenter#431D109
hypocenterC109C2×#431
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C42 ◁ #431

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13122);