Finite Group Databasebeta

C2×D29⋊(C4⋊C8) #16836125

order3712
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D29⋊(C4⋊C8)
unambiguous semidirect productD29⋊(C2×C4⋊C8)

Splittings

SylowC29 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×#1181
commutatorC2×C29C23×C8
FrattiniC22C23×#1181
FittingC2×C42×C29C4
socleC23×C29C22×C4
prime radicalC23×D29C2×C4
cosocleC2×Dic29C24
hypercenterC2×C42#1181
hypocenterC29C22×C4⋊C8
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×C42

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 21143);