Finite Group Databasebeta

C2×#14273645 #16837381

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

Aliases

direct productC2×#14273645

Splittings

SylowC59 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22(C2×D59)⋊C4
commutatorC22×C59C22×C4
FrattiniC2×C4C22×D59
FittingC2×M16×C59C2
socleC22×C59C22⋊C4
prime radicalC23×C59C2×C4
cosocleC2×C4×C59C23
hypercenterC2×M16D59
hypocenterC59C2×#101
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 528);