Finite Group Databasebeta

C2×#11758417 #14521476

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

Aliases

direct productC2×#11758417

Splittings

SylowC31 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#92479
commutator, cosocleC8×C31C23
FrattiniC8C22×D31
FittingC2×Q16×C31C2
socle, prime radicalC22×C31D8
hypercenterC2×Q16D31
hypocenterC31C2×Q32
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#16847567, C4×#11758417, #16847579, …
maximal normal subgroup of#16847567, C4×#11758417, #16847579, …
maximal quotient ofC2×#14520852, C2×#14520853, C2×#14520874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 976);