Finite Group Databasebeta

#440×D109 #28371807

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

Aliases

direct product#440×D109

Splittings

Fitting#440×C109 ⋊ C2
SylowC109 ⋊ C2×#440

Subgroups

subgroupG/H
centerC22C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#440×C109C2
socleC22×C109C22×D4
prime radicalC2×D4×D109C22
cosocleC2×C4×C109C24
hypercenter#440D109
hypocenterC109C2×#440
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #440

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

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, 13285);