Finite Group Databasebeta

C4×#11745664 #16837355

order3776
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#11745664

Splittings

SylowC59 ⋊ C4×M16

Subgroups

subgroupG/H
centerC42C2×D59
commutatorC2×C59C2×C42
FrattiniC2×C4C22×D59
FittingC2×C42×C59C2
socleC22×C59C22×C4
prime radicalC23×C59C2×C4
cosocleC2×C4×C59C23
hypercenterC2×C42D59
hypocenterC59C4×M16
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C42 ◁ C2×C42

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 502);