Finite Group Databasebeta

C22×(C2×D59)⋊C4 #16837849

order3776
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D59)⋊C4

Splittings

FittingC23×C4×C59 ⋊ C2
SylowC59 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D59
commutatorC2×C59C23×C4
FrattiniC22C23×D59
FittingC23×C4×C59C2
socleC24×C59C22
prime radicalC24×D59C2
cosocleC22×C59C24
hypercenterC23×C4D59
hypocenterC59C22×C22⋊C4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4

674 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, 996);