Finite Group Databasebeta

C2×C4⋊C8×D37 #18003145

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

Aliases

direct productC2×C4⋊C8×D37

Splittings

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

Subgroups

subgroupG/H
centerC22×C4C22×D37
commutatorC2×C37C23×C8
FrattiniC2×C4C23×D37
FittingC2×C4⋊C8×C37C2
socleC23×C37C22×C4
prime radicalC23×D37C2×C4
cosocleC2×C4×C37C24
hypercenterC2×C4⋊C8D37
hypocenterC37C22×C4⋊C8
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 13059);