Finite Group Databasebeta

C2×C4×C8×D37 #18002995

order4736
isoclinismisoclinic class of D37
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C8×D37

Splittings

FittingC2×C4×C8×C37 ⋊ C2
derived, SylowC37 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D37
commutator, hypocenterC37C22×C4×C8
FrattiniC2×C4C23×D37
FittingC2×C4×C8×C37C2
socleC23×C37C22×C4
prime radicalC23×D37C2×C4
cosocleC2×C4×C37C24
LCSG ▷ C37
UCSC1 ◁ C2×C4×C8

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

1280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 12909);