Finite Group Databasebeta

C2×#11758467 #14521570

order1984
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#11758467

Splittings

SylowC31 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D31
commutator, cosocleC22×C31C24
FrattiniC22C23×D31
FittingC2×C4⋊C4×C31C2
socle, prime radicalC23×C31C23
hypercenterC2×C4⋊C4D31
hypocenterC31C2×#125
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16846665, #16846667, #16846674, …
maximal normal subgroup of#16846665, #16846667, #16846674, …
maximal quotient ofC2×#14520914, C2×#14520932, C2×#14520936, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 1070);