Finite Group Databasebeta

C2×#11758391 #14520998

order1984
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#11758391

Splittings

SylowC31 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D31
commutatorC2×C31C2×C42
FrattiniC2×C4C22×D31
FittingC2×C42×C31C2
socle, prime radicalC23×C31C2×C4
cosocleC2×C4×C31C23
hypercenterC2×C42D31
hypocenterC31C2×#97
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C42

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16843541, #16843555, #16843592, …
maximal normal subgroup of#16843541, #16843555, #16843592, …
maximal quotient ofC2×#14520771, #16843998, #16844003, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 498);