Finite Group Databasebeta

C2×D37⋊(C4⋊C8) #18011229

order4736
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D37⋊(C4⋊C8)
unambiguous semidirect productD37⋊(C2×C4⋊C8)

Splittings

SylowC37 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×#3866
commutatorC2×C37C23×C8
FrattiniC22C23×#3866
FittingC2×C42×C37C4
socleC23×C37C22×C4
prime radicalC23×D37C2×C4
cosocleC2×Dic37C24
hypercenterC2×C42#3866
hypocenterC37C22×C4⋊C8
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×C42

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21143);