Finite Group Databasebeta

C2×#14557414 #17997017

order4736
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14557414

Splittings

SylowC37 ⋊ C2×#387

Subgroups

subgroupG/H
centerC24C22×D37
commutatorC22×C37C23×C4
FrattiniC23C23×D37
FittingC22×C4⋊C4×C37C2
socle, prime radicalC24×C37C23
cosocleC23×C37C24
hypercenterC22×C4⋊C4D37
hypocenterC37C2×#387
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C24 ◁ C22×C4⋊C4

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 6931);