Finite Group Databasebeta

C2×#14519697 #16839748

order3904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14519697

Splittings

FittingC2×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D61
commutatorC4×C61C22×C4
FrattiniC2×C4C22×D61
FittingC2×C4⋊C4×C61C2
socleC23×C61D4
prime radicalC22×D244C2
cosocleC2×C4×C61C23
hypercenterC2×C4⋊C4D61
hypocenterC61C2×#102
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 535);