Finite Group Databasebeta

C2×#108×D109 #28371633

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

Aliases

direct productC2×#108×D109

Splittings

FittingC2×#108×C109 ⋊ C2
SylowC109 ⋊ C22×#108

Subgroups

subgroupG/H
centerC2×C4D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
FittingC2×#108×C109C2
socleC22×C109C2×C4⋊C4
prime radicalC23×D109Q8
cosocleC2×C4×C109C24
hypercenterC2×#108D109
hypocenterC109C22×#108
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13111);