Finite Group Databasebeta

C2×D109⋊#108 #28379689

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

Aliases

direct productC2×D109⋊#108
unambiguous semidirect productD109⋊(C2×#108)

Splittings

SylowC109 ⋊ C22×#108

Subgroups

subgroupG/H
centerC2×C4C4⋊#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC22×C8×C109C4
socleC22×C109C2×C4⋊C4
prime radicalC23×D109Q8
cosocleC4×D109C24
hypercenterC22×C8#89137
hypocenterC109C22×#108
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 21167);