Finite Group Databasebeta

C2×#11758410 #14521094

order1984
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#11758410

Splittings

SylowC31 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D31
commutatorC4×C31C22×C4
FrattiniC2×C4C22×D31
FittingC2×M16×C31C2
socleC22×C31C4⋊C4
prime radicalC23×C31Q8
cosocleC2×C4×C31C23
hypercenterC2×M16D31
hypocenterC31C2×#108
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16845589, #16845591, #16845594, …
maximal normal subgroup of#16845589, #16845591, #16845594, …
maximal quotient ofC2×#14520799, C2×#14520801, #16844457, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 594);