Finite Group Databasebeta

#430×D109 #28371636

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

Aliases

direct product#430×D109

Splittings

Fitting#430×C109 ⋊ C2
SylowC109 ⋊ C2×#430

Subgroups

subgroupG/H
centerC4C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#430×C109C2
socleC2×C109C22×C4⋊C4
prime radicalC23×D109Q8
cosocleC2×C4×C109C24
hypercenter#430D109
hypocenterC109C2×#430
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13114);