Finite Group Databasebeta

C2×#14273683 #16837855

order3776
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14273683

Splittings

SylowC59 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D59
commutatorC2×C59C23×C4
FrattiniC22C23×D59
FittingC2×C22⋊C4×C59C2
socleC23×C59C23
prime radicalC24×C59C22
cosocleC22×C59C24
hypercenterC2×C22⋊C4D59
hypocenterC59C2×#117
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 1002);