Finite Group Databasebeta

C2×C8×Dic74 #18003517

order4736
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×Dic74

Splittings

SylowC37 ⋊ C2×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C2×D37
commutatorC2×C37C23×C8
FrattiniC2×C4C23×D37
FittingC2×C4×C8×C37C2
socle, prime radicalC23×C37C22×C4
cosocleC2×C4×C37C24
hypercenterC2×C4×C8D37
hypocenterC37C2×C8×Q8
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13431);