Finite Group Databasebeta

C2×#11758415 #14521473

order1984
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11758415

Splittings

SylowC31 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#92479
commutator, cosocleC8×C31C23
FrattiniC8C22×D31
Fitting, prime radicalC2×D8×C31C2
socleC22×C31D8
hypercenterC2×D8D31
hypocenterC31C2×SD32
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#11758415, #16847566, #16847572, …
maximal normal subgroup ofC4×#11758415, #16847566, #16847572, …
maximal quotient ofC2×#14520850, C2×#14520852, C2×#14520876, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 973);