Finite Group Databasebeta

C4×D472 #16837486

order3776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D472

Splittings

FittingC4×C8×C59 ⋊ C2
SylowC59 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C4D236
commutatorC4×C59C22×C4
FrattiniC2×C4C22×D59
FittingC4×C8×C59C2
socleC22×C59C2×D4
prime radicalC2×D472C2
cosocleC2×C4×C59C23
hypercenterC4×C8D59
hypocenterC59C4×D8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 633);