Finite Group Databasebeta

C2×#11758407 #14521095

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

Aliases

direct productC2×#11758407

Splittings

SylowC31 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D124
commutatorC4×C31C22×C4
FrattiniC2×C4C22×D31
FittingC22×C8×C31C2
socleC22×C31C4⋊C4
prime radicalC23×C31Q8
cosocleC2×C4×C31C23
hypercenterC22×C8D31
hypocenterC31C2×#108
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

Relationships

maximal subgroup of#16843804, #16843805, #16843806, …
maximal normal subgroup of#16843804, #16843805, #16843806, …
maximal quotient ofC2×#14520800, C2×#14520802, #16844459, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 595);