Finite Group Databasebeta

C2×#14519800 #16840545

order3904
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14519800

Splittings

FittingC2×Q16×C61 ⋊ C2
SylowC61 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
FittingC2×Q16×C61C2
socleC22×C61C2×D4
hypercenterC2×Q16D61
hypocenterC61C2×#135
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1332);